BIOMECHANICS IN SPORT
PERFORMANCE ENHANCEMENT AND
INJURY PREVENTION
VOLUME IX OF THE ENCYCLOPAEDIA OF SPORTS MEDICINE
AN IOC MEDICAL COMMISSION PUBLICATION
IN COLLABORATION WITH THE
INTERNATIONAL FEDERATION OF SPORTS MEDICINE
EDITED BY
VLADIMIR M. ZATSIORSKY
BIOMECHANICS IN SPORT
IOC MEDICAL COMMISSION
SUB-COMMISSION ON PUBLICATIONS IN THE SPORT SCIENCES
Howard G. Knuttgen PhD (Co-ordinator)
Boston, Massachusetts, USA
Francesco Conconi MD
Ferrara, Italy
Harm Kuipers MD, PhD
Maastricht, The Netherlands
Per A.F.H. Renström MD, PhD
Stockholm, Sweden
Richard H. Strauss MD
Los Angeles, California, USA
BIOMECHANICS IN SPORT
PERFORMANCE ENHANCEMENT AND
INJURY PREVENTION
VOLUME IX OF THE ENCYCLOPAEDIA OF SPORTS MEDICINE
AN IOC MEDICAL COMMISSION PUBLICATION
IN COLLABORATION WITH THE
INTERNATIONAL FEDERATION OF SPORTS MEDICINE
EDITED BY
VLADIMIR M. ZATSIORSKY
© 2000 International Olympic Committee
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Cataloging-in-publication Data
Biomechanics in sport: performance
improvement and injury prevention /
edited by Vladimir M. Zatsiorsky.
p.
cm.—(Volume IX of
the Encyclopaedia of sports medicine)
“An IOC Medical Commission
publication in collaboration with the
International Federation of Sports
Medicine.”
ISBN 0-632-05392-5
1. Sports—Physiological aspects.
2. Human mechanics. 3. Sports
injuries. I. Zatsiorsky, Vladimir M.,
1932– II. IOC Medical Commission.
III. International Federation of Sports
Medicine. IV. Encyclopaedia of sports
medicine; v. 10
RC1235 .B476 2000
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Contents
Part 2: Locomotion
List of Contributors, vii
Forewords, ix
7
Factors Affecting Preferred Rates of Movement
in Cyclic Activities, 143
P.E. MARTIN, D.J. SANDERSON AND
B.R. UMBERGER
8
The Dynamics of Running, 161
K.R. WILLIAMS
9
Resistive Forces in Swimming, 184
A.R. VORONTSOV AND V.A. RUMYANTSEV
Preface, xi
Part 1: Muscle Action in
Sport and Exercise
1
Neural Contributions to Changes in
Muscle Strength, 3
J.G. SEMMLER AND R.M. ENOKA
2
Mechanical Properties and Performance in
Skeletal Muscles, 21
W. HERZOG
3
Muscle-Tendon Architecture and
Athletic Performance, 33
J.H. CHALLIS
4
Eccentric Muscle Action in Sport and
Exercise, 56
B.I. PRILUTSKY
5
Stretch–Shortening Cycle of
Muscle Function, 87
P.V. KOMI AND C. NICOL
6
Biomechanical Foundations of Strength and
Power Training, 103
M.C. SIFF
10
Propulsive Forces in Swimming, 205
A.R. VORONTSOV AND V.A. RUMYANTSEV
11
Performance-Determining Factors in
Speed Skating, 232
J.J. DE KONING AND G.J. VAN INGEN SCHENAU
12
Cross-Country Skiing: Technique, Equipment
and Environmental Factors Affecting
Performance, 247
G.A. SMITH
Part 3: Jumping and
Aerial Movement
13
Aerial Movement, 273
M.R. YEADON
14
The High Jump, 284
J. DAPENA
v
vi
contents
15
Jumping in Figure Skating, 312
D.L. KING
16
Springboard and Platform Diving, 326
D.I. MILLER
17
Determinants of Successful Ski-Jumping
Performance, 349
P.V. KOMI AND M. VIRMAVIRTA
Part 5: Injury Prevention and
Rehabilitation
24
25
Principles of Throwing, 365
R. BARTLETT
19
The Flight of Sports Projectiles, 381
M. HUBBARD
20
Javelin Throwing: an Approach to
Performance Development, 401
K. BARTONIETZ
21
Shot Putting, 435
J. LANKA
22
23
Hammer Throwing: Problems and
Prospects, 458
K. BARTONIETZ
Hitting and Kicking, 487
B.C. ELLIOTT
Musculoskeletal Loading During Landing, 523
J.L. MCNITT-GRAY
26
Sport-Related Spinal Injuries and Their
Prevention, 550
G .- P . B R Ü G G E M A N N
27
Impact Propagation and its Effects on the
Human Body, 577
A.S. VOLOSHIN
28
Neuromechanics of the Initial Phase of
Eccentric Contraction-Induced
Muscle Injury, 588
M.D. GRABINER
Part 4: Throwing and Hitting
18
Mechanisms of Musculoskeletal Injury, 507
R.F. ZERNICKE AND W.C. WHITING
Part 6: Special Olympic Sports
29
Manual Wheelchair Propulsion, 609
L.H.V. VAN DER WOUDE, H.E.J. VEEGER AND
A.J. DALLMEIJER
30
Sports after Amputation, 637
A.S. ARUIN
Index, 651
List of Contributors
A.S. ARUIN PhD, Motion Analysis Laboratory,
Rehabilitation Foundation Inc., 26W171 Roosevelt Road,
Wheaton, IL 60189, USA
R.M. BARTLETT PhD, Sport Science Research
Institute, Sheffield Hallam University, Collegiate Hall,
Sheffield S10 2BP, UK
K. BARTONIETZ PhD, Olympic Training Center
Rhineland-Palatinate/Saarland, Am Sportzentrum 6, 67105
Schifferstadt, Germany
G.-P. BRÜGGEMANN PhD, Deutsche
Sporthochschule Köln, Carl-Diem-Weg 6, 50933 Köln,
Germany
J.H. CHALLIS PhD, Biomechanics Laboratory,
Department of Kinesiology, 39 Rec. Hall, The Pennsylvania
State University, University Park, PA 16802-3408, USA
M.D. GRABINER PhD, Department of Biomedical
Engineering, The Cleveland Clinic Foundation, 9500 Euclid
Avenue, Cleveland, Ohio 44195, USA
W. HERZOG PhD, Faculty of Kinesiology, The
University of Calgary, 2500 University Drive NW, Calgary,
Alberta T2N 1N4, Canada
M. HUBBARD PhD, Department of Mechanical and
Aeronautical Engineering, University of California, Davis,
CA 95616, USA
G.J. van INGEN SCHENAU PhD, Institute
for Fundamental and Clinical Human Movement Sciences,
Faculty of Human Movement Sciences, Vrije Universiteit
Amsterdam, The Netherlands (Professor G.J. van Ingen
Schenau unfortunately passed away during the production
of this volume.)
D.L. KING PhD, Department of Health and Human
A.J. DALLMEIJER PhD, Institute for Fundamental
and Clinical Human Movement Sciences, Faculty of Human
Movement Sciences, Vrije Universiteit Amsterdam, The
Netherlands
Development, Montana State University, Bozeman, MT
59717, USA
P.V. KOMI PhD, Neuromuscular Research Centre,
J. DAPENA PhD, Biomechanics Laboratory,
Department of Biology of Physical Activity, University of
Jyväskylä, 40351 Jyväskylä, Finland
Department of Kinesiology, Indiana University,
Bloomington, IN 47405, USA
J.J. de KONING PhD, Institute for Fundamental and
B. ELLIOTT PhD, The Department of Human
Movement and Exercise Science, The University of Western
Australia, Nedlands, Western Australia 6907, Australia
Clinical Human Movement Sciences, Faculty of Human
Movement Sciences, Vrije Universiteit Amsterdam, The
Netherlands
J. LANKA PhD, Department of Biomechanics, Latvian
R.M. ENOKA PhD, Department of Kinesiology and
Applied Physiology, University of Colorado, Boulder, CO
80309-0354, USA
Academy of Sport Education, Brivibas 333, Riga LV-1006,
Latvia
vii
viii
list of contributors
P.E. MARTIN PhD, Exercise and Sport Research
Institute, Arizona State University, Tempe, Arizona 85287,
USA
H.E.J. VEEGER PhD, Institute for Fundamental and
Clinical Human Movement Sciences, Faculty of Human
Movement Sciences, Vrije Universiteit Amsterdam, The
Netherlands
J.L. McNITT-GRAY PhD, Biomechanics Research
Laboratory, Department of Exercise Sciences, University of
Southern California, Los Angeles, CA 90089-0652, USA
M. VIRMAVIRTA PhLic, Neuromuscular Research
Centre, Department of Biology of Physical Activity,
University of Jyväskylä, 40351 Jyväskylä, Finland
D.I. MILLER PhD, School of Kinesiology, Faculty of
Health Sciences, University of Western Ontario, London,
Ontario, N6A 3K7, Canada
C. NICOL PhD, UMR 6559 Mouvement & Perception,
CNRS-Université de la Méditerranée, Faculté des Sciences
du Sport, 163, avenue de Luminy CP 910, F-13288 Marseille
Cedex 9, France
A.S. VOLOSHIN PhD, Department of Mechanical
Engineering and Mechanics, Institute for Mathematical
Biology and Biomedical Engineering, Lehigh University,
Bethlehem, PA 18015, USA
A.R. VORONTSOV PhD, Department of
Swimming, Russian State Academy of Physical Culture, 4
Sirenevy Boulevard, Moscow 105122, Russian Federation
B.I. PRILUTSKY PhD, Center for Human Movement
Studies, Department of Health and Performance Sciences,
Georgia Institute of Technology, Atlanta, GA 30332, USA
W.C. WHITING PhD, Department of Kinesiology,
California State University, Northridge, 18111 Nordhoff
Street, Northridge, CA 91330-8287 USA
V.A. RUMYANTSEV PhD, Department of
Swimming, Russian State Academy of Physical Culture, 4
Sirenevy Boulevard, Moscow 105122, Russian Federation
K.R. WILLIAMS PhD, Department of Exercise
D.J. SANDERSON PhD, School of Human Kinetics,
L.H.V. van der WOUDE PhD, Institute for
University of British Columbia, Vancouver, British
Columbia, V6T 1Z1, Canada
Science, University of California, Davis, CA 95616, USA
Fundamental and Clinical Human Movement Sciences,
Faculty of Human Movement Sciences, Vrije Universiteit
Amsterdam, The Netherlands
J.G. SEMMLER PhD, Department of Kinesiology and
Applied Physiology, University of Colorado, Boulder, CO
80309-0354, USA
M.R. YEADON PhD, Department of Sports Science,
Loughborough University, Ashby Road, Loughborough,
LE11 3TU, UK
M.C. SIFF PhD, School of Mechanical Engineering,
University of the Witwatersrand, South Africa
G.A. SMITH PhD, Biomechanics Laboratory,
Department of Exercise and Sport Science, Oregon State
University, Corvallis, OR 97331, USA
B.R. UMBERGER MS, Exercise and Sport Research
Institute, Arizona State University, Tempe, Arizona 85287,
USA
V.M. ZATSIORSKY PhD, Department of
Kinesiology, The Pennsylvania State University, University
Park, PA 16802, USA
R.F. ZERNICKE PhD, Faculty of Kinesiology,
University of Calgary, 2500 University Drive NW, Calgary,
AB, T2N 1N4, Canada
Forewords
On behalf of the International Olympic Committee,
I welcome the publication of Volume IX in the IOC
Medical Commission’s series, The Encyclopaedia of
Sports Medicine.
Citius, Altius, Fortius is our motto, which suggests the successful outcome to which all athletes
aspire.
The role of the Olypmic movement is to provide
these athletes with everything they require to attain
this goal.
Biomechanics contributes to this end, through
research into correct movement and the subsequent
improvement in training equipment and techniques,
by always keeping in view ways of improving performance while maintaining absolute respect for the
health of the athletes.
Juan Antonio Samaranch
Président du CIO
Marqués de Samaranch
In the area of sports science, the last 20 years have
witnessed the development of a remarkable number
of advances in our knowledge of skill performance,
equipment design, venue construction, and injury
prevention based on the application of biomechanical principles to sport.
The accumulation of this wealth of biomechanical knowledge demanded that a major publication
be produced to gather, summarize, and interpret
this important work. It therefore became a logical
decision to add ‘biomechanics’ to the list of topic
areas to be addressed in the IOC Medical Commission’s series, The Encyclopaedia of Sports Medicine.
Basic information is provided regarding skeletal
muscle activity in the performance of exercise and
sport; specific sections are devoted to locomotion,
jumping and aerial movement, and throwing; and
particular attention is given to injury prevention,
rehabilitation, and the sports of the Special Olympics.
An effort was made to present the information in a
format and style that would facilitate its practical
application by physicians, coaches, and other professional personnel who work with the science of
sports performance and injury prevention.
This publication will most certainly serve as a
reference and resource for many years to come.
Prince Alexandre de Merode
Chairman, IOC Medical Commission
ix
Preface
The essence of all sports is competition in movement skills and mastership. Sport biomechanics is
the science of sport (athletic) movements. Because
of that, if nothing else, it is vital for sport practice.
For decades, athletic movements have been performed and perfected by the intuition of coaches
and athletes. We do have evidence in the literature
that some practitioners understood the laws of
movement even before Sir Isaac Newton described
them. It was reported that Sancho Panza, when he
saw his famous master attacking the windmills, told
something about Newton’s Third Law: he knew that
the windmills hit his master as brutally as he hit
them. Although it is still possible to find people who
believe that intuitive knowledge in biomechanics is
sufficient to succeed, it is not the prevailing attitude
anymore. More fundamental lore is necessary. I
hope this book proves that.
It was a great honour for me to serve as an editor
of the volume on Biomechanics in Sport: Performance
Enhancement and Injury Prevention. The book is
intended to be a sequel to other volumes of the
series of publications entitled Encyclopaedia of Sports
Medicine that are published under the auspices of the
Medical Commission of the International Olympic
Committee. The main objective of this volume is
to serve coaches, team physicians, and serious
athletes, as well as students concerned with the
problems of sport biomechanics.
Editing the volume was a challenging task: The
first challenge was to decide on the content of the
book. The problems of sport biomechanics can be
clustered in several ways:
• General problems of sport biomechanics (e.g.
muscle biomechanics, eccentric muscle action).
• Given sport movements (high jump) and sports
(biomechanics of diving).
• Parts of the human body (biomechanics of spine).
• Blocks (constitutional parts) of natural athletic
activities (athlete in the air, biomechanics of landing).
Each approach has its own pros and cons; it also
has limitations. For instance, the number of events
in the programme of Summer Olympic Games
exceeds 200. Evidently, it is prohibitive to have 200
chapters covering individual events. After consideration, the plan of the book was selected and
approved by the IOC Publications Advisory Committee (it is my pleasure to thank the Committee
members for their support and useful advice).
The book is divided into the following six parts.
1 Muscle action in sport and exercise: This section
is devoted to general problems of biomechanics of
athletic movements.
2 Locomotion: After the introductory chapter,
which covers material pertinent to all cyclic
locomotions, the following sports are described:
running, cycling, swimming, cross-country skiing,
and skating.
3 Jumping and aerial movement: The opening
chapter in this section highlights the biomechanics
of aerial motion, while other chapters address high
jumping, ski jumping, jumping in figure skating
and diving.
4 Throwing and hitting: The section starts with
two chapters that explain the basic principles of
throwing and the aerodynamic aspects of the flight
xi
xii
preface
of projectiles, respectively. Individual sports are shot
putting, javelin throwing and hammer throwing.
5 Injury prevention and rehabilitation: Each chapter in this section addresses the problems that are
pertinent to many sports.
6 Special Olympics sports: Biomechanics of wheelchair sports and sport for amputees are discussed.
Many recognized scholars participated in this
project. The authors of the volume, 37 in total, have
unique areas of expertise and represent 11 countries, including Austria, Canada, Finland, Germany,
Holland, Latvia, Russia, Singapore, South Africa,
United Kingdom and USA. Geography, however,
did not play a substantial role in determining the
authors. Their expertise did. The book contains
chapters contributed by scholars who have established themselves as prominent world experts in
their particular research or applied fields. To the
extent that certain areas of sport biomechanics
and eminent biomechanists have been omitted,
apologies are offered. Evidently, a line had to be
drawn somewhere. Outstanding experts are, as a
rule, overworked people. Appreciation is acknowledged to the authors of this book who gave of their
precious time to contribute to this endeavour. I am
grateful to all of them.
Vladimir M. Zatsiorsky
Professor
Department of Kinesiology,
The Pennsylvania State University
2000
dedication
A distinguished colleague and friend of the international biomechanics community, Dr. Gerrit Jan van Ingen Schenau, passed away during
the production of this volume. During his academic career, Professor
van Ingen Schenau conducted numerous studies of human performance and contributed dozens of publications to the literature of
human biomechanics and sport. One of his last projects can be found in
this volume, where he was a co-author of Chapter 11, PerformanceDetermining Factors in Speed Skating.
Participation of Professor van Ingen Schenau in international scientific activities will be sorely missed. The contributing authors and I
wish to dedicate this volume to his memory.
VMZ
PART 1
MUSCLE ACTION IN SPORT
AND EXERCISE
Chapter 1
Neural Contributions to Changes in Muscle Strength
J.G. SEMMLER AND R.M. ENOKA
Introduction
To vary the force that a muscle exerts, the nervous
system either changes the number of active motor
units or varies the activation level of those motor
units that have been activated. For much of the
operating range of a muscle, both processes are
activated concurrently (Seyffarth 1940; Person &
Kudina 1972). Motor units are recruited sequentially and the rate at which each discharges action
potentials increases monotonically to some maximal level. Although most human muscles comprise
a few hundred motor units, the order in which
motor units are activated appears to be reasonably
stereotyped (Denny-Brown & Pennybacker 1938;
Henneman 1977; Binder & Mendell 1990). For most
tasks that have been examined, motor units are
recruited in a relatively fixed order that proceeds
from small to large based on differences in motor
neurone size, which is the basis of the Size Principle
(Henneman 1957). Although variation in motor
neurone size per se is not the primary determinant
of differences in recruitment threshold, a number
of properties covary with motor neurone size and
thereby dictate recruitment order (Heckman &
Binder 1993).
Despite current acceptance of the Size Principle as
a rubric for the control of motor unit activity (Cope
& Pinter 1995), our understanding of the distribution of motor unit activity among a group of synergist muscles is more rudimentary. One prominent
example of this deficit in our knowledge is the lack
of understanding of the role performed by the nervous system in the strength gains that are achieved
with physical training. When an individual participates in a strength-training programme, much of
the increase in strength, especially in the first few
weeks of training, is generally attributed to adaptations that occur in the nervous system (Enoka 1988;
Sale 1988). Because the assessment of strength in
humans involves the activation of multiple muscles,
the neural mechanisms that contribute to strength
gains undoubtedly involve the coordination of
motor unit activity within and across muscles. Nonetheless, the evidence that identifies specific neural
mechanisms is rather weak. The purpose of this
chapter is to emphasize our lack of understanding
of the neural mechanisms that mediate strength
gains and to motivate more systematic and critical
studies on this topic.
To accomplish this purpose, we describe the relationship between muscle size and strength, discuss
the significance of specific tension, present the case
for a role of the nervous system in strength gains,
and evaluate the potential neural mechanisms
that contribute to increases in strength. Despite a
substantial literature on training strategies for
increasing muscle strength, less is known about
the biomechanical and physiological mechanisms
responsible for the changes in performance capacity.
Muscle size and strength
Each muscle fibre contains millions of sarcomeres
(the force-generating units of muscle), which are
arranged in series (end-to-end in a myofibril) and
in parallel (side-by-side myofibrils) to one another.
Theoretically, the maximum force that a muscle
3
4
muscle action in sport and exercise
Muscle strength (N)
fibre can exert depends on the number of sarcomeres that are arranged in parallel (Gans & Bock
1965). By extension, the maximum force that a muscle can exert is proportional to the number of muscle
fibres that lie in parallel to one another. Because
of this association, the strength of a muscle can
be estimated anatomically by measuring its crosssectional area (Roy & Edgerton 1991). This measurement should be made perpendicular to the direction
of the muscle fibres and is known as the physiological
cross-sectional area.
Despite the theoretical basis for measuring the
physiological cross-sectional area of muscle to
estimate its force capacity, it is typically more
convenient to measure the anatomical cross-sectional
area, which is a measurement that is made perpendicular to the long axis of the muscle. This can
be accomplished by using one of several imaging
techniques (e.g. computed tomography (CT) scan,
magnetic resonance imaging, ultrasound) to determine the area of a muscle at its maximum diameter. Examples of the relationship between muscle
strength and anatomical cross-sectional area are
shown in Fig. 1.1 (Kanehisa et al. 1994). In these
240
240
200
200
160
160
120
120
80
80
40
6
8
10
12
14
16
18
20
40
6
10
14
18
22
26
30
200
40
50
60
70
80
90
100
(a)
(b)
700
800
600
700
500
600
400
500
300
400
200
300
100
(c)
30
40
50
60
70
80
100
(d)
Muscle cross-sectional area (cm2)
Fig. 1.1 Muscle strength varies as a function of the cross-sectional area of a muscle (adapted from Kanehisa et al. 1994).
(a) Elbow flexors (r2 = 0.56). (b) Elbow extensors (r2 = 0.61). (c) Knee flexors (r2 = 0.17 for men [solid line] and 0.35 for
women [dashed line]). (d) Knee extensors (r2 = 0.54 for men and 0.40 for women). Men are indicated with filled symbols
and women with open symbols.
muscle strength
experiments, muscle strength was measured as the
peak force exerted on an isokinetic device at an
angular velocity of about 1.0 rad · s−1, and the maximum anatomical cross-sectional area for each
muscle group was measured with an ultrasound
machine. Measurements were made on the elbow
flexor and extensor muscles and on the knee flexor
and extensor muscles of 27 men and 26 women.
For the elbow flexor and extensor muscles, the
men were, on average, stronger than the women,
but this was due to a greater cross-sectional area
(Fig. 1.1a,b). The average strength (mean ± SE) of the
elbow flexors, for example, was 130 ± 4 N for the
men compared with 89 ± 4 N for the women; and
the average cross-sectional area was 141 ± 0.4 cm2
for the men and 91 ± 0.2 cm2 for the women. Thus,
the normalized force (force/cross-sectional area) was
9.2 N · cm–2 for men and 9.8 N · cm–2 for women. In
contrast, the differences in strength between men
and women for the knee muscles (Fig. 1.1c,d) were
due to differences in both the cross-sectional area
and the normalized force (force per unit area). For
example, the average strength for the knee extensor
muscles was 477 ± 17 N for the men and 317 ± 15 N
for the women, and the average cross-sectional area
was 74 ± 2 cm2 for the men and 62 ± 2 cm2 for the
women. The normalized forces were 6.5 N · cm−2
and 5.1 N · cm–2, respectively. The difference in
normalized force is apparent by the y-axis displacement of the regression lines for the men and women
(Fig. 1.1c,d). These regression lines indicate that for
a cross-sectional area of 70 cm2 for the knee extensor
muscles, a man could exert a force of 461 N compared with 361 N for a woman.
These data demonstrate, as many others have
shown (Jones et al. 1989; Keen et al. 1994; Kawakami
et al. 1995; Narici et al. 1996), that the strength of a
muscle depends at least partly on its size, as characterized by its cross-sectional area. This conclusion
provides the foundation for the strength-training
strategy of designing exercise programmes that maximize muscle hypertrophy, i.e. an increase in the
number of force-generating units that are arranged
in parallel. Nonetheless, there is substantial variability in the relationship between strength and crosssectional area, which is indicated by the scatter of
the data points about the lines of best fit in Fig. 1.1.
5
Some of this variability may be due to the use of
anatomical rather than physiological cross-sectional
area as the index of muscle size. However, variation
in cross-sectional area accounts for only about 50%
of the difference in strength between individuals
(Jones et al. 1989; Narici et al. 1996).
Specific tension
The other muscular factor that influences strength is
the intrinsic force-generating capacity of the muscle
fibres. This property is known as specific tension and
is expressed as the force that a muscle fibre can exert
per unit of cross-sectional area (N · cm–2). To make
this measurement in human subjects, segments of
muscle fibres are obtained by muscle biopsy and
attached to a sensitive force transducer that is
mounted on a microscope (Larsson & Salviati 1992).
Based on such measurements, specific tension has
been found to vary with muscle fibre types, to
decrease after 6 weeks of bed rest for all fibre types,
to decline selectively with ageing, and to increase
for some fibre types with sprint training (Harridge
et al. 1996, 1998; Larsson et al. 1996, 1997). For example, the specific tension of an average type II
muscle fibre in vastus lateralis was greater than
that for a type I muscle fibre for the young and
active old adults but not for the sedentary old
adults (Table 1.1). This finding indicates that the
maximum force capacity of a type II muscle fibre
Table 1.1 Cross-sectional area (µm2) and specific tension
(N · cm−2) of chemically skinned fibre segments from the
human vastus lateralis muscle (Larsson et al. 1997).
Cross-sectional
area
Specific tension
Subject group
Type I
Type II
Type I
Type II
Young control
2820
± 620
3840
± 740
19
±3
24*
±3
Old control
3090
± 870
2770†
± 740
18
±6
19
±1
Old active
2870
± 680
3710
± 1570
16
±5
20*
±6
Values are mean ± SD. * P < 0.001 for type I vs. type II.
† P < 0.001 for old control vs. young control and old active.
6
muscle action in sport and exercise
in an old adult who is sedentary is less than that for
young and active old adults because it is smaller
(cross-sectional area) and it has a lower specific
tension. Although such variations in specific tension probably contribute to the variability in the
relationship between strength and cross-sectional
area (Fig. 1.1), the relative role of differences in specific tension is unknown but is probably significant.
There are at least two mechanisms that can
account for variations in specific tension. These
are the density of the myofilaments in the muscle
fibre and the efficacy of force transmission from
the sarcomeres to the skeleton. The density of
myofilaments can be measured from electron
microscopy images of muscle fibres obtained from a
biopsy sample. One of the few studies on this issue
found that although 6 weeks of training increased
the strength (18%) and cross-sectional area (11%) of
the knee extensor muscles, there was no increase in
myofilament density (Claasen et al. 1989). This was
expressed as no change after training in the distance
between myosin filaments (~38 nm) or in the ratio
of actin to myosin filaments (~3.9). However,
some caution is necessary in the interpretation of
these data because the fixation procedures may
have influenced the outcome variables. Nonetheless, even if these data are accurate, it is unknown if
myofilament density changes with longer duration
training programmes or with different types of
exercise protocols (e.g. eccentric contractions, electrical stimulation, plyometric training).
Besides myofilament density, specific tension can
also be influenced by variation in the structural elements that transmit force from the sarcomeres to
the skeleton. This process involves the cytoskeletal
proteins, which provide connections between
myofilaments, between sarcomeres within a myofibril, between myofibrils and the sarcolemma, and
between muscle fibres and associated connective
tissues (Patel & Lieber 1997). Within the sarcomere,
for example, the protein titin keeps the myofilaments aligned, which produces the banding structure of skeletal muscle and probably contributes
significantly to the passive tension of muscle (Wang
et al. 1993). Furthermore, there are several different
isoforms of titin (Granzier et al. 1996), which may
have different mechanical properties. Similarly, the
intermediate fibres, which include the proteins
desmin, vimentin and skelemin, are arranged longitudinally along and transversely across sarcomeres,
between the myofibrils within a muscle fibre, and
between muscle fibres (Patel & Lieber 1997). The
intermediate fibres are probably responsible for the
alignment of adjacent sarcomeres and undoubtedly
provide a pathway for the longitudinal and lateral
transmission of force between sarcomeres, myofibrils
and muscle fibres. Because much of the force generated by the contractile proteins is transmitted laterally (Street 1983), variation in the intermediate fibres
could contribute to differences in specific tension.
In contrast to changes in specific tension at the
muscle-fibre level, some investigators determine
‘specific tension’ at the whole-muscle level by normalizing muscle force relative to the cross-sectional
area of the muscle. This is misleading because the
normalized force depends critically on the efficacy of
the mechanisms that mediate excitation-contraction
coupling. For example, Kandarian and colleagues
found that the decline in normalized force exhibited
by a hypertrophied soleus muscle was largely due
to an impairment of calcium delivery to the contractile apparatus and not due to changes in the intrinsic
force-generating capacity of muscle (Kandarian &
White 1989; Kandarian & Williams 1993). For this
reason, it is necessary to distinguish between the
normalized force of a whole muscle and the specific
tension of a single muscle fibre.
Although there is some uncertainty over the
mechanisms that underlie the variation in specific
tension of muscle fibres, it is clear that this factor can
contribute significantly to differences in strength
among individuals. Nonetheless, the magnitude
of this effect is probably specific to each muscle
(namely fibre-type proportions) and to the physical
activity levels of the individual.
Evidence for a role of the nervous system
in strength gains
Two sets of observations can be used to argue for
a role by the nervous system in training-induced
changes in muscle strength. These are the dissociation
between changes in muscle size and strength and
the specificity of the improvements in performance.
muscle strength
4
Normalized strength
Dissociated changes in muscle size and strength
3
2
1
0
(a)
CSA (µm2)
8000
6000
4000
2000
(b)
50
Muscle fibre types (%)
When an individual participates in a strengthtraining programme or experiences a decline in
physical activity, the accompanying change in muscle strength precedes and exceeds the change in
muscle size (Häkkinen et al. 1985; Narici et al. 1989).
For example, although the loads that subjects could
lift increased over an 8-week training period by
100 –200%, there were no changes in the crosssectional areas of muscle fibres in the vastus lateralis muscle (Staron et al. 1994). The maximum load
that the men and women could lift in the squat
exercise increased by about 200% (Fig. 1.2a), yet
the size of the type I, IIa and IIb fibres did not
increase significantly (Fig. 1.2b). However, there
was a decrease in the proportion of the type IIb
muscle fibres after 2 weeks of training for women
and after 4 weeks of training for men (Fig. 1.2c),
which may have influenced the average specific
tension of the fibres in the muscle. Nonetheless,
there was an increase in strength in the first few
weeks of training that was not accompanied by an
increase in muscle size or a change in the fibre-type
proportions. By default, many investigators interpret this dissociation as evidence of a contribution
to strength gains by so-called ‘neural factors’.
Similarly, when muscle is subjected to a period
of reduced use (e.g. bed rest, limb immobilization,
tenotomy), the decline in strength is greater than the
loss of muscle mass (Duchateau 1995; Berg et al.
1997; Yue et al. 1997). For example, a patient who
sustained a closed bimalleolar fracture experienced
a 25% decrease in the cross-sectional area of the triceps surae muscles after 8 weeks of immobilization
but a 50% decline in muscle strength (Vandenborne
et al. 1998). Furthermore, the force exerted by the
triceps surae muscle was increased by an electric
shock that was superimposed on a maximum
voluntary contraction. Such dissociations between
muscle size and strength are also evident in healthy
subjects who experience a period of reduced use
(Duchateau & Hainaut 1987).
Perhaps the most convincing case for a dissociation between muscle size and strength is made
by findings that it is possible to increase muscle
strength without even subjecting the muscle to
7
40
30
20
10
0
(c)
0
2
4
6
8
Time (weeks)
Fig. 1.2 Changes in strength, muscle fibre size, and
fibre-type proportions over the course of an 8-week
training programme (adapted from Staron et al. 1994).
(a) Normalized strength (1RM load relative to fat-free
mass) for the squat lift. (b) Cross-sectional areas (CSA) of
muscle fibres from vastus lateralis. (c) The proportion (%)
of the different muscle fibre types. Men are indicated with
filled symbols and women with open symbols. In (b) and
(c), type I fibres are shown with squares, type IIa fibres
with circles, and type IIb fibres with triangles.
8
muscle action in sport and exercise
Untrained
Trained
Force (% pre-training)
40
30
20
10
0
Imagined Contraction
Control
(a)
Imagined Contraction
Control
Subject group
80
Isometric
Non-isometric
Electromyostimulation
70
Strength change in untrained limb (%)
60
50
40
30
20
10
0
–10
–20
(b)
0
10
20
30
40
Strength change in trained limb (%)
physical training. Two protocols underscore this
type of adaptation: imagined contractions and
cross-education. When compared with subjects
who either did no training or performed a 4-week
strength-training programme, subjects who practised sets of imagined maximum voluntary contractions experienced a significant increase in the
strength of a hand muscle (Yue & Cole 1992; however, cf. Herbert et al. 1998). Although electromyo-
50
60
Fig. 1.3 The strength of a muscle can
increase in the absence of physical
training. (a) Increases (mean ± SD)
in the maximum abduction force of
the fifth finger after training with real
or imagined maximal contractions
(adapted from Yue & Cole 1992).
Training was performed with the left
hand but strength was measured in
both hands. (b) Changes in muscle
strength in homologous muscles of
both limbs after training with a single
limb. The data are derived from
29 studies reported in the literature.
gram (EMG) measurements indicated that the hand
muscle was not activated during the training with
imagined contractions, strength increased after 20
training sessions. The maximum abduction force
exerted by the fifth finger increased by 30 ± 7% for
the subjects who actually performed contractions,
by 22 ± 11% for the subjects who did the imagined
contractions, and by 4 ± 6% for the subjects who
did no training (Fig. 1.3a). Furthermore, the abduc-
muscle strength
tion strength of the contralateral (untrained) fifth
finger increased by 14 ± 12%, 11 ± 9%, and 2 ± 7%,
respectively.
The training effect that occurred in the untrained
hand represents a phenomenon known as crosseducation. Most studies that have examined this
effect report that when the muscles in one limb
participate in a strength-training programme, the
homologous muscles also experience a significant
increase in muscle strength despite the absence of
activation during the training programme and no
change in muscle fibre characteristics. For the data
shown in Fig. 1.3b, the average increase in muscle
strength for the trained limb was 24 ± 13% compared with an average of 16 ± 15% for the untrained
limb. The magnitude of the cross-education effect
was more variable for non-isometric contractions
(21 ± 20%) compared with isometric contractions
(14 ± 9%). Cross-education has also been demonstrated as a reduction in the quantity of muscle
mass that is activated to lift submaximal loads after
9 weeks of unilateral strength training (Ploutz et al.
1994).
Specificity of strength gains
If the strength of a muscle is primarily dependent on
its size, then whenever the muscle is activated maximally the peak force should be about the same. The
fact that this is not the case underscores the dissociation between muscle size and strength and provides
evidence for a significant contribution to strength
gains from neural mechanisms. Whenever a muscle
participates in a strength-training programme, the
improvement in performance depends on the similarity between the training and testing procedures
(Almåsbakk & Hoff 1996; Wilson et al. 1996). This
effect, known as the specificity of training, is
often demonstrated by comparing training-induced
increases in the peak force exerted during a maximum isometric contraction with the maximum
load that can be lifted once (1 repetition maximum
[1RM] load). For example, when 11 men and 9
women trained the knee extensor muscles for 12
weeks by raising and lowering a load, the 1RM
load increased by 200% for the men and 240% for
the women compared with increases in the max-
9
imum isometric force of 20% for the men and 4% for
the women (Rutherford & Jones 1986). Similarly,
when Jones and Rutherford (1987) trained another
group of subjects (11 men, 1 woman) with isometric,
concentric, or eccentric contractions, the subjects
who trained with eccentric contractions increased
their 1RM load by 261% and maximum isometric
force by 11%. Furthermore, the subjects who trained
with isometric contractions experienced the greatest
increase (35% vs. 11% and 15%) in the maximum
isometric force.
The specificity of training is also evident with
other training modalities. For example, O’Hagan et
al. (1995) found that subjects who trained the elbow
flexor muscles for 20 weeks on a device that provided a hydraulic resistance experienced significant
increases in muscle cross-sectional area but taskdependent increases in muscle strength (Fig. 1.4).
As determined by CT scan, the increase in crosssectional area was greater for the brachialis muscle
than the biceps brachii muscle, for both the men and
women. The increases in peak force on the hydraulic
device at the speed used in training and the
increases in the maximum load that could be lifted
once (1RM load) were about 50% for the men and
120% for the women. In contrast, the peak torque
exerted on an isokinetic dynamometer at four
angular velocities was largely unaffected (< 25%
increase) by the training programme.
The specificity effects appear to be most pronounced for tasks that require more learning, such
as less constrained movements (Rutherford & Jones
1986; Wilson et al. 1996; Chilibeck et al. 1998), those
involving voluntary activation compared with electrical stimulation (McDonagh et al. 1983; Young et al.
1985), and those involving eccentric contractions
(Higbie et al. 1996). For example, Hortobágyi et al.
(1996) examined the adaptations in the forcevelocity domain after subjects performed 36 training sessions on an isokinetic dynamometer over a
12-week period with the knee extensor muscles of
the left leg. Some subjects trained with concentric
contractions while others trained with eccentric
contractions. For the subjects who trained with
concentric contractions, the increase in peak force
at a knee angle of 2.36 rad was similar for eccentric
(46%), isometric (34%), and concentric (53%)
10
muscle action in sport and exercise
120
Men
Elbow flexors (% increase)
100
Women
Fig. 1.4 Changes in the size and
strength of the elbow flexor muscles
in men and women after 20 weeks
of training (adapted from O’Hagan
et al. 1995). Muscle size was
characterized by the measurement
of cross-sectional area (CSA) for
the brachialis and biceps brachii
muscles. Muscle strength was
represented by the peak force
exerted on a hydraulic device,
the 1RM load, and the peak torque
on an isokinetic dynamometer
(240 degrees · s–1).
80
60
40
20
0
–20
Brachialis
CSA
Biceps brachii
CSA
Hydraulic
force
1-RM load
contractions. In contrast, the subjects who trained
with eccentric contractions experienced a much
greater increase in the peak force during eccentric
contractions (116%) compared with isometric (48%)
and concentric (29%) contractions. Furthermore, the
cross-education effect was greatest for the subjects
in the eccentric group when performing eccentric
contractions (Hortobágyi et al. 1997).
These studies on the specificity of training
demonstrate that improvements in strength-based
performance are often unrelated to changes in muscle size. This dissociation is usually attributed to
adaptations that occur in the nervous system, such
as those associated with learning and improvements in coordination (Rutherford & Jones 1986;
Laidlaw et al. 1999).
Isokinetic
torque
Right
Left
Supraspinal centres
1
5
4
3
INe
6
8
2
INf
INe
INf
4
MNe
MNf
Neural activation of muscle
7
Despite the evidence that suggests a significant role
for neural mechanisms in strength-training adaptations, it has proven difficult to identify specific
mechanisms that underlie these changes. Figure 1.5
proposes sites within the nervous system where
adaptations may occur, as suggested by current
research findings. The proposed mechanisms range
from a simple increase in the quantity of the neural
drive to more subtle variations in the timing of
motor unit activation. There is no consensus in
the literature, however, on a significant role for any
single mechanism.
Fig. 1.5 Scheme of the distribution of neural adaptations
after strength training of the knee extensors of the right leg
for 8 weeks. The numbers indicate the potential sites
within the nervous system at which adaptations might
occur, as suggested by various experimental findings:
(1) enhanced output from supraspinal centres as suggested
muscle strength
11
Table 1.2 Percentage increases in performance and EMG for isometric contractions, 1RM contractions, and vertical jumps
after 6 months of strength training by middle-aged (~40 years) and old (~70 years) men and women. (Adapted from
Häkkinen et al. 1998.)
Isometric
contraction
1RM contraction
Vertical jump
Subject group
Force
EMG
Load
EMG
Height
EMG
Men
Middle-aged
Old
36 ± 4
36 ± 3
28 ± 13
33 ± 8
22 ± 2
21 ± 3
26 ± 13
15 ± 8
11 ± 8
24 ± 8
19 ± 12
14 ± 6
Women
Middle-aged
Old
66 ± 9
57 ± 10
48 ± 13
33 ± 12
34 ± 4
30 ± 3
32 ± 14
24 ± 12
14 ± 4
18 ± 6
21 ± 7
34 ± 7
Values are mean ± SE. The EMG is based on the sum of the rectified and
smoothed value for the vastus medialis and vastus lateralis of the right leg. All
increases were statistically significant. Data provided by Dr. Keijo Häkkinen.
Activation maximality
Perhaps the most obvious neural adaptation that
might contribute to strength gains is an increase in
the quantity of the neural drive to muscle during
a maximum contraction (sites 1, 6 and 7 in Fig. 1.5).
This possibility has been examined by measuring
changes in the absolute magnitude of the EMG and
by testing activation maximality with the twitch interpolation technique. Although numerous investigators
by findings on imagined contractions; (2) altered drive
that reduces coactivation of the antagonist muscles;
(3) modified drive that causes greater activation of the
muscles that assist the prime movers; (4) more effective
coupling in spinal interneuronal pathways between limbs
that produces cross-education; (5) changes in the
descending drive that influence the bilateral deficit;
(6) coupling of the input to motor neurones that raises the
degree of synchronization in the discharge of action
potentials; (7) greater muscle activation as indicated by an
increased EMG, perhaps due to greater neural drive or a
more effective excitation-contraction coupling for the
same level of activation; and (8) heightened excitability
of motor neurones as indicated by reflex potentiation
and motor neurone plasticity. Abbreviations: INe,
interneurones that project to the motor neurones
innervating extensor muscles; INf, interneurones that
project to the motor neurones innervating flexor muscles;
MNe , motor neurones innervating the extensor muscles;
and MNf, motor neurones innervating the flexor muscles.
have compared the EMG before and after strength
training as an index of changes in the neural drive,
the results are equivocal. Some studies have found
significant increases in EMG amplitude after several
weeks of training (Narici et al. 1989; Häkkinen et al.
1998), some have found task-specific increases in
EMG (Thépaut-Mathieu et al. 1988; Higbie et al.
1996; Hortobágyi et al. 1996), and some have found
no change in the EMG (Carolan & Cafarelli 1992).
One of the reasons for such diverse results is
the variability associated with EMG measurements
across subjects and sessions. The absolute amplitude of an EMG signal, for example, can vary across
sessions due to such factors as differences in the
placement of the electrodes and changes in the
impedance of the skin and subcutaneous tissue.
This variability can be reduced by averaging the
EMG from several recording sites over a single
muscle (Clancy & Hogan 1995) or by normalizing
the recorded signal relative to the M wave (Keen
et al. 1994). For example, when Häkkinen et al. (1998)
summed the rectified and integrated EMG across
the vastus lateralis and vastus medialis muscles,
they detected significant training-related increases
in the EMG for isometric contractions, for lifts with
1RM loads, and for maximum vertical jumps in
various groups of subjects (Table 1.2). Similarly,
Higbie et al. (1996) found significant increases in
12
muscle action in sport and exercise
the summed EMG of vastus medialis and vastus
lateralis after 10 weeks of strength training on an
isokinetic device. The increase in EMG, however,
was specific to the training task. For example, subjects who trained with eccentric contractions experienced a 36% increase in the peak torque and a 17%
increase in the EMG during eccentric contractions
but increases of only 7% for the peak torque and
EMG during concentric contractions.
Others, however, have found that the increase in
EMG peaked after a few weeks of training whereas
strength continued to increase for the duration of
the training programme. For example, Keen et al.
(1994) found that linear improvements in the
strength of a hand muscle were associated with a
non-monotonic increase in the average EMG. In
both young and old adults, the maximum voluntary
contraction (MVC) force increased by about 40%
after 12 weeks of strength training but the average
EMG, when normalized to the peak-to-peak M wave,
peaked at week 8 and was not different from initial
values at week 12 for both groups of subjects. The
normalized EMG increased by 10% at week 8 compared with an increase of 15–20% for MVC force.
Because muscle volume only increased by 7% in
this study, the increase in MVC force over the final
4 weeks of training must have been due to other
factors.
Alternatively, the adaptation might involve a
greater activation of the available muscle mass for
the same EMG input (site 7 in Fig. 1.5). This possibility requires that individuals be unable to maximally
activate muscle in an untrained state; the evidence
on this issue is mixed. When the maximality of a
contraction is tested by superimposing an electric
shock (interpolated twitch) on an MVC, most investigators (Merton 1954; Bélanger & McComas 1981;
Rutherford et al. 1986; Herbert & Gandevia 1996;
De Serres & Enoka 1998), but not all (Dowling et al.
1994; Kent-Braun and Le Blanc 1996), find that subjects can maximally activate a muscle with a voluntary command. For example, subjects appear able to
exert, on average, about 95% of the maximum force,
and in 25% of the trials the force was indeed maximal (Allen et al. 1995). In contrast, when wholemuscle activation was assessed by measuring the
transverse relaxation time (T2) of muscle water with
magnetic resonance imaging (Fisher et al. 1990;
Tesch 1993; Yue et al. 1994; Ray & Dudley 1998), the
MVC torque of the knee extensors seemed to be
achievable by activating only ~71% of the crosssectional area of the quadriceps femoris muscles
(Adams et al. 1993). Similarly, the discharge rates of
motor units during high-force contractions appear
to place the motor units on the upper part of the
force–frequency relationship but not on the plateau
(Enoka 1995). These observations suggest that the
force exerted during an MVC is less than the maximum tetanic force, but the magnitude of the difference is unclear.
Coactivation of antagonist muscles
In contrast to the apparent lack of an association
between changes in strength and whole-muscle
EMG, strength training does seem to affect the function of the relevant motor neurone pools. These
changes can involve both the relative activation of
different motor neurone pools and the connectivity
within and between pools (Fig. 1.5). For example,
strength training, at least with isometric contractions, appears to involve a reduction in the coactivation of the antagonist muscle (site 2 in Fig. 1.5)
within the first week or so of training (Carolan &
Cafarelli 1992). Similarly, elite athletes exhibit
reduced coactivation of the semitendinosus muscle
compared with sedentary subjects when performing isokinetic contractions with the knee extensor
muscles (Amiridis et al. 1996). As a consequence, the
net torque about a joint will increase due to removal
of the negative torque contributed by the antagonist
muscle. In short-term training studies, however,
the reduction in coactivation is minimal. Häkkinen
et al. (1998) found that substantial increases in knee
extensor strength after 6 months of training were
accompanied by mixed declines in coactivation of
the antagonist muscle (biceps femoris). Coactivation of biceps femoris during an isometric MVC
did not change in middle-aged men and women,
whereas it declined by an average of 3% and 7% in
older men and women, respectively. Furthermore,
there was no change in coactivation during the
muscle strength
1RM task for all groups except the older women.
Although these changes in antagonist activation
may occur at the level of the descending drive from
the supraspinal centres (site 3 in Fig. 1.5), they do
not appear to be significant contributors to shortterm increases in muscle strength.
Spinal cord plasticity
Of all the purported neural mechanisms, the
most convincing case can be made for changes in
neuronal connectivity with strength training. Two
examples underscore this adaptation. The first
example is related to the phenomenon of crosseducation (site 4 in Fig. 1.5). In normally active
individuals, the maximum force that a muscle can
exert decreases when the homologous muscle in the
contralateral limb is activated concurrently (Ohtsuki
1983; Secher et al. 1988; Schantz et al. 1989; however,
cf. Jakobi & Cafarelli 1998). This effect is known as
the bilateral deficit and appears to be caused by neural interactions between the limbs (site 5 in Fig. 1.5;
Howard & Enoka 1991). The magnitude of this
effect is usually small (5–10%), but can be quite substantial (25 – 45%), especially for rapid contractions
(Koh et al. 1993). Because the size of the deficit can be
altered by training (Taniguchi 1998), it is considered
to depend on the neural connections between limbs.
For example, individuals who train both limbs concurrently (e.g. rowers, weightlifters) exhibit a bilateral facilitation rather than a deficit (Secher 1975;
Howard & Enoka 1991). In these subjects, muscle
force is maximal during bilateral rather than unilateral contractions. This adaptation is presumably
mediated by the long-term patterns of muscle
activation that affect the descending drive to the
interneuronal pools (Fig. 1.5).
The second example of neuronal plasticity concerns the connections between motor neurones in
the same pool (site 6 in Fig. 1.5). Despite initial
reports to the contrary, the discharge of action
potentials by a motor neurone is temporally related
to the discharge by other motor neurones. The
degree of association can be quantified as the measurement of motor unit synchronization (Sears &
Stagg 1976; Datta & Stephens 1990; Nordstrom et al.
13
1992), which indicates the patterns of shared synaptic input onto motor neurones either directly
or through last-order interneurones (Kirkwood
et al. 1982). The magnitude of this synchronized
discharge among motor units is variable and
is influenced by such factors as the task that is
examined, the motor units and muscles involved
in the task, and the type of habitual physical activity performed by the individual (Bremner et al.
1991; Schmied et al. 1994; Semmler & Nordstrom
1995, 1998; Huesler et al. 1998). The level of synchronization appears to be reduced between
motor units in the individuals who require greater
independent control of the fingers. This includes
musicians and the dominant hand of control subjects (Semmler & Nordstrom 1998). In contrast,
motor unit synchronization is greater among
motor units in the hand muscles of individuals
who consistently perform strength-training activities
(Milner-Brown et al. 1975; Semmler & Nordstrom
1998). Nonetheless, computer simulations by Yao
et al. (2000) indicate that motor unit synchronization
does not increase the maximum force exerted by a
muscle during steady-state isometric contractions
(Fig. 1.6).
The altered connectivity among neurones as a
consequence of training is also evident through the
testing of reflexes (site 8 in Fig. 1.5). When an electric
shock sufficient to elicit a maximal M wave (compound muscle action potential) is applied to a muscle nerve during an MVC, two reflex responses (V1
and V2) can also be elicited. Initial studies of these
responses normalized them to the maximal M wave
and used the ratio as an index of reflex potentiation
(Sale 1988). Reflex potentiation (enhancement of V1
and V2) was found to occur in all muscles, to be
more pronounced in weightlifters than sprinters,
to increase with strength training, and to decrease
with limb immobilization (Sale et al. 1982; Sale
1988). Subsequent work by Wolpaw and colleagues
on operant conditioning of the spinal stretch reflex
and the H reflex suggests that much of this plasticity
appears to be located in the spinal cord, to involve
the motor neurones, and also to be expressed in the
contralateral, untrained limb (Wolpaw & Lee 1989;
Carp & Wolpaw 1994; Wolpaw 1994).
14
muscle action in sport and exercise
120
110
100
90
80
70
60
50
40
30
20
10
2 mV
2000 au
1s
1s
Fig. 1.6 Comparison of the EMG and force from computer simulations of maximal isometric contractions in the presence
(right column) and absence (left column) of motor unit synchronization. In each column, the top set of traces indicate the
timing of the action potentials discharged by some of the motor neurones in the pool (n = 120), the middle trace shows the
interference EMG, and the bottom trace represents the net force. Adjusting the timing (synchronization), but not the
number, of action potentials had a marked effect on the amplitude of the simulated EMG, no effect on the average
simulated force, and a significant effect on the smoothness of the force profile.
muscle strength
These studies demonstrate that participation in
a strength-training programme can induce changes
in the connections between motor neurones located
in the spinal cord. These adaptations are manifested as cross-education, the bilateral deficit (or
facilitation), motor unit synchronization, and reflex
potentiation. Nonetheless, the contributions of such
changes to increases in muscle strength remain
unknown.
Coordination
One of the most oft-cited reasons for an increase in
strength is an improved coordination among the
muscles involved in the task. A role for coordination
is often invoked when strength gains are found to
be specific to the training task (Rutherford & Jones
1986; Chilibeck et al. 1998). For example, subjects
who performed strength-training exercises with a
hand muscle (first dorsal interosseus) for 8 weeks
experienced a 33% increase in the MVC force but
only an 11% increase in the tetanic force evoked by
electrical stimulation of the muscle (Davies et al.
1985). Furthermore, when another group of subjects
trained the muscle with electrical stimulation for
8 weeks, there was no change in the evoked tetanic
force whereas the MVC force declined by 11%
(Davies et al. 1985). Because electrical stimulation
evokes a muscle contraction by generating action
potentials in intramuscular axonal branches, such
findings suggest that activation by the nervous
system is important in the expression of muscle
strength.
A significant role of training-induced changes
in neural activation can also be made based on
post-training improvements in submaximal performance. One such example involves the steadiness of submaximal isometric contractions. When
subjects exert an abduction force with the index
finger, the normalized force fluctuations (coefficient of variation) are usually greater for older
adults compared with younger adults, especially
at low forces (Galganski et al. 1993). After participation in a strength-training programme, however, the steadiness exhibited by the older adults
improved and was similar to that of younger adults
15
(Keen et al. 1994). Because this improvement in
performance was not associated with a change in
the distribution of motor unit forces, the adaptations may have involved an enhancement of the
muscle activation by the nervous system. Another
example of the training-induced improvement in
submaximal performance is the reduced volume
of muscle that was activated to lift a submaximal
load after participation in a strength-training programme (Ploutz et al. 1994). This effect appears to
be largely mediated by neural mechanisms because there was no hypertrophy of the different
muscle fibre types and the improvement was also
evident in the untrained contralateral knee extensor
muscles.
These findings suggest that the coordination of
activity within and across muscles has a significant
influence on the expression of muscle strength. In
general, such adaptations influence two features of
a strength manoeuvre: the postural foundation for
the task and the goal-directed movement itself.
Because the human body can be characterized as a
linked mechanical system, it is necessary to orientate the body segments and to set the base of support on which the movement is performed (Horak &
Macpherson 1996). For example, the elbow flexor
muscles could lift a hand-held load with the body
in a variety of postures, including standing, sitting,
prone or supine positions. Such variations in posture appear to influence the outcome of a training
programme, as indicated in several studies on the
specificity of training. In one of the most comprehensive studies on this issue, Wilson et al. (1996) had
subjects train for 8 weeks and then examined the
improvement in performance of several tasks. They
found, for example, increases of 21% for the squat
lift and the vertical-jump height, but only a 10%
increase in a 6-second-test on a cycle ergometer and
no change in the performance by the knee extensor
muscles on an isokinetic test. The improvements in
performance were greatest in the tests involving
postures that were used during training. Despite
this recognized role for the specificity of posture, no
studies have explicitly demonstrated a significant
role for adaptations in postural support as contributing to strength gain.
16
muscle action in sport and exercise
Hip
2
1
5
6
3
4
Knee
Fig. 1.7 Model of the human leg with six muscles
arranged around the hip and knee joints. Muscles 1 to 4
cross one joint while muscles 5 and 6 cross both joints.
(From van Ingen Schenau et al. 1990; Fig. 41.6.)
Similarly, muscles that act across other joints can
influence the mechanical action about a joint. The
classic example of this effect is the use of two-joint
muscles to distribute net moments and to transfer
power between joints (van Ingen Schenau et al.
1992). This scheme is represented in Fig. 1.7, where
the human leg is modelled as a pelvis, thigh and
shank with several one- and two-joint muscles crossing the hip and knee joints. In this model, muscles 1
and 3 are one-joint hip and knee extensors, muscles
2 and 4 are one-joint hip and knee flexors, and muscles 5 and 6 are two-joint muscles. Concurrent hip
and knee extension can be performed by activation
of the two one-joint extensors (muscles 1 and 3).
Because muscle 5 exerts a flexor torque about the
hip joint and an extensor torque about the knee, concurrent activation of muscle 5 with muscles 1 and
3 will result in a reduction in the net torque at the
hip but an increase in the net torque at the knee.
Based on this interaction, the two-joint muscle
is described as redistributing some of the muscle
torque and joint power from the hip to the knee.
Conversely, activation of muscle 6 will result in
redistribution from the knee to the hip. Although
rarely considered, such interactions are undoubtedly
significant in the measurement of muscle strength.
In addition to the postural support and the transfer of actions between joints, an improvement in
coordination can involve an enhancement of the
timing of motor unit and muscle activity. At the
motor-unit level, for example, van Cutsem et al.
(1998) found that the gains obtained by training with
rapid, low-load contractions involved reductions in
the recruitment threshold, increases in motor unit
force, and an increased rate of action-potential discharge. Twelve weeks of training the dorsiflexor
muscles resulted in a pronounced increase in the
initial discharge rate of motor units and an improvement in the maximal rate of force development.
Similarly, although the timing of action potentials
between motor units (motor unit synchronization)
does not increase steady-state force, it may influence
the rate of increase in force. Because of technical
limitations, the magnitude of motor unit synchronization during anisometric contractions is unknown. However, there must be some functional
benefit from short-term synchronization because it
is greater in a hand muscle of weightlifters (MilnerBrown et al. 1975; Semmler & Nordstrom 1998) and
it increases during the performance of attentiondemanding tasks (Schmied et al. 1998).
At the whole-muscle level, the timing issues
related to coordination involve task-specific variation in the activation of muscle. For example, the relative EMG amplitude in biceps brachii, brachialis
and brachioradialis varied for constant-force (isometric) and constant-load (isoinertial) conditions
despite a similar net elbow-flexor torque (Buchanan
& Lloyd 1995). Similarly, the relative EMG activity
of brachioradialis and biceps brachii varied for
shortening and lengthening contractions (Nakazawa
et al. 1993) and the relative contributions of motor
unit recruitment and modulation of discharge rate
varied for shortening and lengthening contractions
(Kossev & Christova 1998). Presumably, early gains
in a strength-training programme are related to
learning the appropriate activation pattern for the
task, especially if it is a novel task.
muscle strength
Conclusion
Although a compelling case can be made for a
significant role of adaptations in the nervous system
for training-induced increases in muscle strength,
the specific mechanisms remain elusive. There is
neither a consensus on individual mechanisms nor
evidence that suggests the relative significance of
the various mechanisms. These deficits in our know-
17
ledge exist partly because of technical limitations
but mainly because of the narrow view taken in the
search for neural mechanisms.
Acknowledgements
This work was partially supported by a grant from
the National Institutes of Health (AG 13929) that
was awarded to RME.
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Chapter 2
Mechanical Properties and Performance
in Skeletal Muscles
W. HERZOG
Introduction
The mechanical properties of skeletal muscle determine its performance. Mechanical properties are
defined here as those properties of skeletal muscle
that can be measured by parameters derived from
mechanics: force, length, velocity, work and power.
The performance achieved in many sports depends
to a large degree on these parameters, for example,
on the power an athlete can produce or the velocity
(speed) he or she can achieve or impart on an implement. Human joints are typically crossed by many
muscles; therefore, athletic performance depends
typically on the properties of many muscles, as well
as their exact coordination. Coordination is defined
here as the interaction of the force–time histories of
muscles that contribute to a movement, and thus,
because of the geometry of the musculoskeletal system, the moment–time histories of these muscles
about joints. The coordination of muscles is tremendously important for achieving precise movements
or movements that maximize the work performed
or the power produced, features that are of primary significance for optimal performance in many
sports. However, coordination of muscles is an
issue of motor control rather than mechanics; it will
only be included in this chapter when required for
clarity.
Despite the well-accepted relationship between
the mechanical properties of skeletal muscle and
performance in many sports, there is a sparsity of
muscle mechanics research in sports. Also, in the
practical application of physical training aimed at
improving sport performance, athletes and coaches
rarely consider the mechanical properties of skeletal
muscles with the exception of force (strength);
strength training is a well-accepted mode for
improving muscular strength. The reasons for this
rather sad state of affairs is not clear; however, the
following factors might be partly responsible for
the lack of muscle mechanics research in sport.
• Most mechanical properties of skeletal muscle are
non-linear, therefore their mathematical description
is not always trivial.
• It is virtually impossible to determine even the
most basic properties of individual skeletal muscles
in vivo and non-invasively.
• The time dependence of the mechanical properties (e.g. with increasing fatigue) are virtually
unknown.
Because muscle mechanics research in sports is
rare, it is not appropriate to write a literature review here. Such a review would reveal a sketchy,
incomplete picture that might confuse rather than
enlighten, or worse yet, might lead to inappropriate
interpretations and generalizations. Therefore, the
goals of this chapter are:
• to present some basic considerations regarding
the mechanical properties of skeletal muscle; and
• to give examples of how principles of muscle
mechanics might be applied to evaluate or improve
sports performance
Basic considerations
In this section, five considerations regarding muscle
mechanics will be presented. First, the proposed
mechanism of muscular force production is
21
22
muscle action in sport and exercise
introduced. From this mechanism, many mechanical properties of muscle can be derived directly.
Second, selected mechanical properties of skeletal
muscle are introduced. Third, the in vitro or in situ
mechanical properties of skeletal muscle derived
from laboratory experiment cannot be directly used
for in vivo human skeletal muscles. Selected examples will be shown to illustrate this point. Fourth,
athletes are injured frequently or have musculoskeletal pain. It is discussed how pain and injury
might influence muscular performance. Fifth, skeletal muscle is a biological tissue with a tremendous
ability to adapt. Issues of muscular adaptation and
the possible influence of such adaptations are discussed. Increases in mass and strength of muscles,
arguably the most important factor for muscular
performance, will be deliberately omitted from this
discussion because this topic is covered elsewhere
in this book and would require too much space for
proper coverage. Here, we discuss muscular adaptations that are typically ignored in sports sciences.
Mechanism of muscular force production
The accepted mechanism of muscular contraction
and force production is the sliding filament theory
(Huxley & Hanson 1954; Huxley & Niedergerke
1954) combined with the cross-bridge theory
(Huxley 1957; Huxley & Simmons 1971). According to the sliding filament theory, shortening and
lengthening of muscle is brought about by the sliding of actin relative to myosin filaments. Force transmission from the myosin to the actin filament is
thought to occur by a series of periodically arranged
myosin-sidepieces (the cross-bridges) that can
attach to periodically arranged, specialized sites on
the actin filament. Some of the basic assumptions
underlying the cross-bridge theory that are directly
relevant for deriving the mechanical properties of
skeletal muscle are:
• cross-bridges are periodically arranged on the
myosin filament;
• cross-bridges attach to specialized sites that are
periodically arranged on the actin filament;
• each cross-bridge produces the same average
force and has the same capacity to perform mechanical work;
Equilibrium position
of M site
Myosin filament
O M
Actin filament
A
x
Fig. 2.1 Schematic illustration of a cross-bridge link
between myosin and actin filaments as proposed by
Huxley (1957). The so-called ‘x-distance’ is defined as the
distance from the cross-bridge equilibrium position (O)
to the nearest cross-bridge attachment site on the actin
filament (A). (Reprinted from Huxley (1957), pp. 255–318,
with permission from Elsevier Science.)
• actin and myosin filaments are essentially rigid;
• cross-bridges attach and detach according to rate
functions that are dependent exclusively on the
so-called ‘x-distance’, the distance from the crossbridge head in its equilibrium position (Fig. 2.1) to
the nearest attachment site (A in Fig. 2.1) on the
actin filament;
• the instantaneous force of a cross-bridge depends
on the x-distance exclusively; and
• each cross-bridge cycle is associated with the
hydrolysation of one adenosine triphosphate (ATP).
For a thorough review of the cross-bridge theory
and its mathematical formulation, the reader is
referred to Huxley (1957), Huxley and Simmons
(1971), Pollack (1990) and Epstein and Herzog
(1998).
When expressing the cross-bridge theory mathematically, mechanical parameters such as the
force, work or the energy required for a given
contractile process can be calculated. Also, many
of the mechanical properties can be derived directly
from the cross-bridge theory. For example, the
shape and extent of the so-called plateau and
descending limb of the sarcomere force–length
relationship (Gordon et al. 1966), and the concentric
part of the force–velocity relationship observed
experimentally (Hill 1938) can be approximated
and explained by the theory. However, it must be
pointed out that many experimental observations
skeletal muscle performance
cannot be explained or are not part of the original
formulation of the cross-bridge theory; such observations include the long-lasting effects of contraction history on force, or the heat production and
force during eccentric contraction. Nevertheless, the
cross-bridge theory provides, at present, the best
basis for understanding and explaining the mechanical properties of skeletal muscle.
Although it may be argued that there is no need
for athletes and coaches to understand the crossbridge theory in its details, it should be recognized
that muscular properties and performance in a
given situation can be predicted reasonably well
when equipped with some basic knowledge of the
mechanisms underlying muscular contraction. The
mechanical properties arising from the cross-bridge
model should be known by every coach as they
might influence sport performance dramatically.
Mechanical properties of skeletal muscle
Five mechanical properties of skeletal muscle will
be discussed here. Only the basic characteristics of
these properties are emphasized. Details that are not
directly relevant for muscular or sport performance
are ignored, therefore the following must be viewed
as a ‘simplified’ or ‘textbook’ version of reality,
Force
the force–length relationship
The force–length relationship of skeletal muscle
relates the maximal, isometric force to length. The
term ‘isometric’ may relate to any specified level.
For example, when talking about the muscle or sarcomere force–length relationship, the whole muscle
or the sarcomeres are kept at a constant length,
respectively. The force–length relationship is a static
property of skeletal muscle; that means, a point on
the force–length relationship is obtained by setting
the muscle length, activating the muscle maximally,
and then measuring the corresponding steady-state
force (Fig. 2.2a). In order to obtain a second point,
the muscle is relaxed (deactivated), set at the new
length of interest and then reactivated maximally.
It is not possible to go from point 1 (F1) to point
2 (F2) along the force–length relationship (Fig. 2.2b),
F1
L2
F2
F2
0
(a)
and other references should be consulted if more
detailed information is sought. The five properties
introduced here include:
• the force–length relationship;
• the force–velocity relationship;
• the power–velocity relationship;
• the endurance time–stress relationship; and
• selected history-dependent force properties.
L1
F1
t0
23
Time
0
(b)
L1
L2
Length
Fig. 2.2 Schematic illustration of how force–length relationships of muscles are determined, thereby emphasizing the
static, non-continuous nature of the force–length relationship. (a) Force–time curves for two separate, fully activated
contractions, one at a length L1, the other at a length L2. In both contractions, a steady-state force is measured, F1 and F2,
respectively. (b) Force–length curve illustrating how the results of the experiment shown in (a) are used to determine the
force–length relationship. Note that it is not possible to take a fully activated muscle and stretch it from L1 to L2 (or shorten
it from L2 to L1) such that the force trace follows that shown in (b), because of the static, discontinuous nature of the
force–length relationship.
24
muscle action in sport and exercise
Ascending
limb
100
3
4
2
Force (%)
athlete therefore is of utmost importance for success
in bicycling (Yoshihuku & Herzog 1990).
Plateau
region
Descending
limb
the force–velocity relationship
50
5
1
0
2.17
1.27
3.6
Sarcomere length (µm)
2.00
1.70
Fig. 2.3 Sarcomere force–length relationship as first
described by Gordon et al. (1966) for frog skeletal muscle.
The force–velocity relationship describes the relation between the maximal force at optimal length
(the length at which the muscle can exert its maximal isometric force) and the corresponding speed
of muscle shortening. For shortening (concentric)
contractions, the force–velocity relationship has
been described in mathematical form for over 60
years (Fenn & Marsh 1935; Hill 1938). In fact, Hill’s
(1938) force–velocity equation is still used today
more often than any other equation to describe the
force–velocity relationship of shortening muscle. It
states:
F=
except, possibly, if the length change was carefully
controlled by a complex and varying activation of
the muscle during the experiment.
The sarcomere force–length relationship may be
derived accurately based on the cross-bridge
theory (Gordon et al. 1966). Specifically, the plateau
region and the descending limb of the force–length
relationship can be determined directly from the
amount of myofilament overlap and the assumptions of the cross-bridge theory that: (i) the actin
and myosin filaments are essentially rigid; (ii) they
have periodically aligned attachment sites and
cross-bridges, respectively; and (iii) each crossbridge exerts the same amount of force and work
independently of other cross-bridges and its own
time history (Fig. 2.3).
In principle, the muscle force–length relationship
states that the maximal force of a muscle depends on
its length. In the human musculoskeletal system, the
length of a muscle can be related to the angle(s) of
the joint(s) the muscle is crossing. Therefore, there
is an optimal length or joint angle at which muscular force is maximal. Knowing this length may
be important for optimal sport performances. For
example, during bicycling, the geometry of the bike
dictates directly over which range of the force–
length relationship the leg muscles work. Choosing
the appropriate bike geometry for each individual
F0 b − av
b+v
(2.1)
where F is the maximal force of a muscle at optimal
length, F0 is the maximal isometric force at optimal
length, v is the speed of shortening, and a and b are
constants with units of force (N) and speed (m · s–1),
respectively. A corresponding well-accepted equation for the force–velocity relationship of lengthening (eccentric) contractions does not exist.
For concentric contractions, the maximal force a
muscle can produce at optimal length decreases
with increasing speeds of shortening (Fig. 2.4) until
it reaches a critical speed, v0, at which the external
Force
Fmax
F0
V0
Velongation
Fig. 2.4 Schematic force–velocity relationship for
shortening and lengthening muscle.
Vshortening
skeletal muscle performance
force of the muscle becomes zero. The speed, v0, can
be calculated from Eqn 2.1 by setting F to zero,
therefore:
v0 =
F0 b
a
(2.2)
For eccentric contractions, the force a muscle can
exert increases with increasing speeds of lengthening until a critical speed is reached at which the
force becomes constant independent of the speed
and equals about 1.5–2.0 times the maximal isometric force at optimal length, F0 (Fig. 2.4). Since the
force of a muscle depends on its contractile speed,
force also depends on movement speed. For example, it has been well described that the force that can
be exerted on the pedals during bicycling decreases
with increasing speed of pedalling (Hull & Jorge
1985; Patterson & Moreno 1990; Sanderson 1991).
The shape of the force–velocity relationship
depends strongly on the fibre type distribution
within a muscle. Although the force per crosssectional area (stress) of a slow-twitch and fasttwitch muscle fibre is about the same, the maximal
speed of shortening differs by a factor of about 2
(Fig. 2.5). Therefore, for a given speed of shortening a predominantly fast-twitch fibred muscle can
exert more force than a predominantly slow-twitch
fibred muscle, although their isometric force (per
cross-sectional area) is about equal. This observation explains why athletes with a high percentage
of fast-twitch fibres typically perform better than
athletes with a high percentage of slow-twitch fibres
in events where a high speed of movement execution is combined with high force requirements—
for example, in all sprinting, throwing and jumping
events of track and field.
the power–velocity relationship
The power–velocity relationship can be derived
directly from the force–velocity relationship since
power, P, is the vector dot product of force (F, vector) and velocity (v, vector):
P=F·v
(2.3)
which might be reduced to the scalar multiplication
of the force magnitude, F, and the speed, v, for the
special case of power in a skeletal muscle; i.e.
P = Fv
(2.4)
For concentric contractions, the power a muscle can
exert is zero for isometric contractions (because v =
0) and for contractions at the maximal speed of
shortening, v0 (because F = 0). Power output of a
muscle reaches a peak at a speed of about 30% of the
maximal speed of shortening (Fig. 2.6). Therefore, in
an athletic event in which power output should be
maximized, it is of advantage to perform the movement at such a speed (if possible) that the major
muscles contributing to the task contract at about
30% of their maximal speed of shortening. It has
been suggested that animals take advantage of the
Force
Force/power
Power
Force
Slow
Fast
Velocity
0.0
0.3
1.0
Velocity
Fig. 2.5 Schematic force–velocity relationship for
shortening contractions of a slow-twitch and a fast-twitch
muscle fibre.
25
Fig. 2.6 Force–velocity and corresponding
power–velocity relationship for shortening muscle.
26
muscle action in sport and exercise
power–velocity relationship of their muscles when
escaping from predators. For example, it has been
proposed that the frog leg muscles that contribute to
jumping all contract close to 30% of their maximal
shortening velocity, and so are able to produce near
maximal power output of the legs (Lutz & Rome
1993). Quick, large jumps are taken by frogs to avoid
being eaten by predators.
In some sports, movement speed can be selected
by the athletes. Again, I would like to use the example of bicycling. When cycling at 40 km · h–1, the
athlete has a variety of gear ratios available to produce a given power output. Therefore, the athlete
can directly manipulate movement speed (pedalling
rate) for a given performance (cycling at 40 km · h–1).
The choice of proper gearing (pedalling rate) may be
a decisive factor in the success of a cyclist.
the endurance time–stress relationship
Force/stress
The three properties of skeletal muscle discussed
so far do not take fatigue into account. Fatigue
of skeletal muscle is defined here as the inability
of a muscle to maintain a required force. Fatigue
occurs fast when a muscle exerts large forces (or
stresses). Maximal forces may only be sustained
for a few seconds. However, a muscle that exerts
a very small force relative to its maximal force
may do so for an almost infinite amount of time
(Fig. 2.7).
A predominantly slow-twitch fibred muscle
Slow fibre
Fast fibre
Time
Fig. 2.7 Schematic force/stress–time relationship for a
fast-twitch and a slow-twitch fibre.
can maintain a given amount of stress for a
longer period of time than a predominantly fasttwitch fibred muscle (Fig. 2.7). Therefore, athletes
with predominantly slow-twitch fibred muscles
typically perform better than athletes with predominantly fast-twitched fibred muscles in sports
that require long periods of muscular involvement at relatively low force levels—for example,
long-distance running.
selected history-dependent properties
History-dependent properties of skeletal muscles
have largely been ignored in muscle mechanics
despite the fact that they have been observed experimentally and well described for at least half a
century (e.g. Abbott & Aubert 1952; Maréchal &
Plaghki 1979; Edman & Tsuchiya 1996; Herzog &
Leonard 1997). History-dependent properties refer
to properties of skeletal muscle (e.g. its ability to
produce force) that depend on the contractile history. These properties are dynamic in nature and
therefore are different from the static properties
described so far.
The two history-dependent properties selected
for this chapter are the force depression following
muscle shortening and the force enhancement
following muscle stretching. Force depression following muscle shortening refers to the observed
phenomenon that the isometric force following
muscle shortening is reduced compared with the
corresponding purely isometric force (Fig. 2.8).
Although this phenomenon has been well accepted
for a long time (Abbott & Aubert 1952; Maréchal &
Plaghki 1979) the mechanism causing force depression is not understood (Maréchal & Plaghki 1979;
Herzog 1998). Also, force depression following
muscle shortening has only recently been observed
in human skeletal muscle (De Ruiter et al. 1998) and
has been demonstrated to occur during voluntary
human contractions in only a single study to date
(Lee et al. 1999).
Force enhancement following muscle elongation
refers to the experimentally observed result that the
isometric force following muscle stretch is higher
and remains higher than the corresponding purely
skeletal muscle performance
27
Isometric
∆F
Lengthening
Force
Force
Shortening
Isometric
Time
Length
Length
Time
∆F
Time
Time
Fig. 2.8 Schematic illustration of force depression
following muscle shortening. When comparing the
maximal force of a purely isometric contraction to that of
an isometric contraction that is preceded by a shortening
of the muscle, it is observed that the isometric force
following shortening is decreased (∆F) compared with the
purely isometric force at the corresponding muscle length.
isometric force (Fig. 2.9). Force enhancement following muscle stretch has only been observed in
artificially stimulated non-human muscle preparations (Abbott & Aubert 1952; Edman & Tsuchiya
1996); therefore, the possible significance of this
property in human skeletal muscle during voluntary contractions must still be established. Nevertheless, the idea that stretching a muscle before
concentric use might be beneficial for performance
enhancement appears attractive and is used by
many athletes. For example, movements such as a
golf swing, jumping or throwing of any object are
typically (if the rules of the game allow and if time
permits) preceded by a counter-movement in which
the major muscles required for the task are actively
prestretched.
Fig. 2.9 Schematic illustration of force enhancement
following muscle lengthening. When comparing the
maximal force of a purely isometric contraction to that of
an isometric contraction that is preceded by a lengthening
of the muscle, it is observed that the isometric force
following lengthening is increased (∆F) compared with
the purely isometric force at the corresponding muscle
length.
Muscle properties in humans
(special considerations)
With few exceptions, the mechanical properties
of skeletal muscles described in the previous
section were obtained from isolated preparations
of animal muscles. Human muscles may differ
from animal muscles, and furthermore human
muscles are voluntarily activated in sports and
exercise rather than artificially stimulated. Therefore, some of the properties described above
might only apply to a limited degree to in vivo
human skeletal muscles. I would like to give two
conceptual examples why in vivo human skeletal
muscle properties may differ substantially from
those of isolated in situ (or in vitro) animal muscles.
28
muscle action in sport and exercise
These two conceptual examples may be broadly
grouped into activation- and adaptation-dependent
phenomena.
activation-dependent phenomena
When determining force–length, force–velocity,
power–velocity, stress-endurance time, or historydependent phenomena of isolated skeletal muscles,
activation of the muscle is controlled, constant and
artificial. Muscular contractions during human
movement, and sport, are voluntary, and even maximal contractions are not performed at constant
levels of activation. It has been proposed that during
human voluntary contractions, activation may be
increased when a muscle or muscle group contracts
at full effort but the contractile conditions are not
well-suited for large force production. For example,
Hasler et al. (1994) argued that maximal voluntary
activation of the knee extensor muscles (as recorded
by surface electromyography, EMG) was increased
towards full knee extension compared with levels of
EMG at intermediate knee angles. The increase in
EMG activity towards full knee extension was interpreted as an attempt of the neural control system to
partly offset the unfavourable contractile conditions
of the knee extensors at or near the fully extended
knee.
Also, during maximal effort eccentric knee extensor contractions, the knee extensors should be
1.5–2.0 times as strong as during maximal effort isometric contractions, but they are not. Knee extensor
activation is inhibited in this situation (presumably
for reasons of safety) such that the eccentric force
is about the same as that produced isometrically at
the corresponding lengths (Westing et al. 1990).
Finally, pain or injury may not allow athletes to
fully activate their muscles. For example, anterior
knee pain, knee ligament injury, and knee effusion
have all been shown to reduce the activation of the
knee extensors achieved during maximal voluntary
contractions in normal people and athletes (Suter
et al. 1996; Huber et al. 1998). All these factors must
be considered when assessing the potential for
force, work and power output of muscles during
athletic activities.
adaptation-dependent phenomena
Although the mechanical properties of skeletal
muscle, such as the force–length and force–velocity
relationships, are typically treated as constant,
invariant properties, it is well recognized that
muscular properties may adapt to the requirements of everyday exercise and athletic training.
For example, the force–length properties of highperformance cyclists and runners were found to differ significantly between the two groups of athletes,
and appeared to have adapted to maximize cycling
and running performance, respectively (Herzog et al.
1991a). Adaptations of strength following strength
training and of endurance following aerobic training of skeletal muscles are other well-documented
and well-accepted adaptations in athletes. These
examples should serve to illustrate the possible danger of transferring muscle properties determined on
in situ or in vitro preparations to the in vivo musculature of human athletes during competition.
Selected examples
Few examples exist in which muscle properties or
muscle mechanics were used thoroughly and systematically to gain insight into the performance of
an athlete or to maximize performance in a given
sport. The possible exception to this rule is bicycling. Bicycling is an attractive sport to study from
a muscle mechanics point of view because it is
an essentially two-dimensional motion with few
degrees of freedom. It can easily and realistically be
studied in the laboratory, and output measures of
mechanical performance (power, force, speed) can
be determined in a straightforward way. Corresponding physiological measures, particularly those
relating to the energetics of bicycling, have been
determined for years using well-established testing
procedures. Therefore, bicycling appears in many of
the examples cited in the following pages.
When seated, the excursions of a cyclist’s lower
limb joints are basically given by the geometry of
the bicycle, particularly the seat height, the handle
bar length and the crank length. Therefore, the
excursions of the lower limb muscles, as well as the
skeletal muscle performance
maintenance of maximal power for about 15 –20 s in
a 200 m sprint with the corresponding preparation
phase), or the goals in long-distance cycling require
different pedalling rates for success. Although pedalling at 60 r.p.m. uses less oxygen than pedalling
at higher rates, the power that can be produced
at 60 r.p.m. is relatively low because for a given
(high) power output, the pedal forces need to be
high causing local muscular fatigue to occur quickly.
Sprinting at 150 r.p.m. on the track or 120 r.p.m.
during road racing allows for a high power output
with relatively small muscular forces. However,
at these high pedalling rates oxygen consumption
for a given power output becomes prohibitive,
and so this cannot be the strategy of choice for
long-distance riding. Riding at 90 r.p.m. is a good
compromise between the force–velocity, power–
velocity and endurance time–stress relationships,
although why most top cyclists prefer to ride at or
near 90 r.p.m. still awaits complete and satisfactory
explanation.
For maximal power output, athletes should use
the primary muscles required for the task at optimal
muscle length, at the optimal speed of shortening, and preferably after a stretch of the muscle
(Fig. 2.10). Obviously, the musculoskeletal system is
not built exclusively to maximize performance in
a given sport, such as bicycling. However, muscles
probably adapt to everyday exercise and training. The force–length properties of the human
rectus femoris (RF) in cyclists are negative, those
Length
Force
Force
Force/power
area of the force–length relationship over which the
lower limb muscles are working during a full pedal
revolution is, to a large extent, given by the bicycle
geometry and the anatomy of the athlete. In the
ideal case, bicycle geometry should be chosen such
that all major cycling muscles operate at or near the
plateau region of the force–length relationship. It
has been determined theoretically that such a geometry is achieved when the seat height is about
510 mm and the crank length is about 170 mm for
a subject with thigh and shank length of 430 and
440 mm, respectively (Andrews 1987; Yoshihuku &
Herzog 1996).
Once the bicycle geometry is set, the speed of
muscular contraction depends exclusively on the
pedalling rate. For minimal oxygen consumption,
pedalling rates of 50–65 revolutions per minute
(r.p.m.) have been shown to be optimal (Seabury et
al. 1977; Coast & Welch 1985; Marsh & Martin 1993).
Power output on a street bicycle (free gear selection)
is maximized at about 120 r.p.m. (Sargeant et al.
1981; McCartney et al. 1983; Beelen & Sargeant 1991;
MacIntosh & MacEachern 1997) and on a track bicycle (no gear selection, 200 m sprint) at about 150
r.p.m. (Yoshihuku & Herzog 1990). Finally, during
long-distance racing, top athletes prefer to pedal
at rates of about 90 r.p.m. (Hagberg et al. 1981;
Patterson & Moreno 1990; Marsh & Martin 1993).
According to the power–velocity relationship, a
pedalling rate of about 120 r.p.m. would be optimal.
However, the constraints of track cycling (one gear,
29
Velocity
Time
Fig. 2.10 Schematic force–length, force/power–velocity, and force–time curves illustrating that for maximal muscle
power output, a muscle should be at a length close to optimal, should shorten at a speed close to optimal (i.e. at about 30%
of the maximal speed of shortening), and should be used following a muscle stretch.
30
muscle action in sport and exercise
Runners
Force
Force
Cyclists
Length
Length
Fig. 2.11 Schematic illustration of the experimentally observed force–length relationships of human rectus femoris
muscles in elite cyclists and elite runners.
of runners are positive (Herzog et al. 1991a), indicating that bicyclists are relatively stronger at short RF
lengths and runners are relatively stronger at long
RF lengths, as required for cycling and running,
respectively (Fig. 2.11). This observation suggests
that RF properties adapted in these athletes to
accommodate the everyday demands of training
and exercise. It has been speculated that such an
adaptation could have occurred because of a change
in the sarcomeres that are arranged in series in the
RF fibres of these athletes (Herzog et al. 1991a), an
attractive but as yet unproven speculation.
Independent of the mechanism of the muscular
adaptation, it is safe to suggest that the RF force–
length properties of the cyclists are not optimal for
running and vice versa. This result has two interesting implications. First, cycling is not a good
cross-training for running and vice versa, or in more
general terms, cross-training could limit performance in the target sport. Second, in multievent
sports, such as triathlon, even the most talented athlete will likely never be able to compete with the
specialists in a particular discipline. For example,
a highly talented runner who turns to triathlon
cannot run with world-class runners even if the
running training in terms of time, mileage and
attempted intensity is the same for the triathlete as
for the runners. The reason is not the amount or
intensity of running but the fact that the properties
of the leg musculature will likely never be optimal
for running because the triathlete also swims and
cycles.
Final comments
Strength, power and endurance are attributes of
skeletal muscles that often determine athletic success. The physiological adaptations of muscle to
strength- and endurance-training are well known
and documented. It was not the intent of this
chapter to review the corresponding literature
here. However, strength, power and endurance of a
muscle are dramatically influenced by the length,
speed and contractile history. This influence might
be evaluated by knowing some of the mechanical
properties of in vivo human skeletal muscles. Here, I
have attempted to introduce some of these properties and demonstrate with selected examples how
they might influence sport performance.
Two main difficulties arise when attempting to
relate the properties of skeletal muscle to athletic
performance:
• very little is known about the properties of individual, in vivo human skeletal muscles; and
• very little is known about the contractile conditions of the major task-specific muscles in sports.
Therefore, the current chapter cannot be viewed
as a textbook chapter with all the answers. Rather, it
skeletal muscle performance
represents considerations that might turn out to be
useful in the analysis of the biomechanics of sports.
It is hoped that this chapter might motivate sports
biomechanists to systematically and thoroughly
31
investigate sports activities and performances in the
light of muscle mechanics. This approach is sorely
lacking and offers new opportunities to gain exciting insights into the biomechanics of sports.
References
Abbott, B.C. & Aubert, X.M. (1952) The
force exerted by active striated muscle
during and after change of length.
Journal of Physiology 117, 77–86.
Andrews, J.G. (1987) The functional roles
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Beelen, A. & Sargeant, A.J. (1991) Effect of
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(2), 583–591.
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Models of Skeletal Muscle: Biological and
Mathematical Considerations. John Wiley,
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Fenn, W.O. & Marsh, B.O. (1935) Muscular
force at different speeds of shortening.
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Gordon, A.M., Huxley, A.F. & Julian, F.J.
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with sarcomere length in vertebrate
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23, 108–114.
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Bicycle pedalling forces as a function of
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during steady-rate cycling in
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(1981) Maximum leg force and power
output during short-term dynamic
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1175 –1182.
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Extent of motor unit activation in the
32
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quadriceps muscles of healthy subjects.
Muscle and Nerve 19, 1046–1048.
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on eccentric and concentric torquevelocity relationships during knee
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Yoshihuku, Y. & Herzog, W. (1990) Optimal
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Maximal muscle power output in
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14, 139 –157.
Chapter 3
Muscle-Tendon Architecture and
Athletic Performance
J.H. CHALLIS
Introduction
Athletic activities place a wide range of demands on
the human muscular system. Some activities require
small amounts of muscle force adjusted in fine
increments, some require the rapid production of
high forces, while yet others demand the slow production of very high forces. The purpose of this
chapter is to identify the key properties of muscle
and explain how they influence muscle function
during athletic activities. The focus will be on skeletal muscle as opposed to the other two forms of
muscle, smooth and cardiac, as skeletal muscle can
be controlled voluntarily. As the skeletal muscle
system has to perform a variety of functions its
design is generally a compromise; it is specialized
only in the sense that it can perform a variety of
tasks.
Newton’s First Law basically states that we need
forces to stop, start or alter motion, therefore as the
muscle fibres are the sources of force production in
the human body they are responsible for our voluntary movement or lack of it. The muscle fibres produce forces which are transmitted via tendons to
the skeleton, and transformation of these forces
to moments at the joints either causes motion or
restrains motion caused by other forces (e.g. maintaining upright posture when standing in a strong
breeze). Therefore, it is useful not only to consider
the forces the muscles produce but also to analyse
how these muscles operate across joints. When
referring to muscle-tendon architecture we are
referring to the structure and arrangement of the
components of the muscle-tendon system. This
chapter will examine how the muscle-tendon system is arranged to produce movement, and the
structures that permit this.
The contractile machinery
Reference is often made to ‘muscle’ when we are
really referring to a muscle-tendon complex. The
muscle-tendon complex is composed of muscle
fibres, which are the actively controlled force generators that are attached to the skeleton via lengths of
tendon at either end of the muscle belly. There are a
variety of ways in which the muscle fibres can orientate themselves to the tendon. This aspect of their
organization can be very important, as can the relative amounts of tendon and muscle fibre composing
the muscle-tendon unit; these will be reviewed later.
It is the building blocks of the muscle fibres, the
myofilaments, which reveal the properties of the
muscle fibres and these will be reviewed in this
section.
We are all familiar with skeletal muscles as our
own musculoskeletal system contains nearly 700 of
them, and we come across it everyday in the form of
meat. The whole muscle is surrounded by a layer
of connective tissue, the fascia, beneath which is a
further sheath of connective tissue, the epimysium.
Whole muscle is composed of a large number of fascicles, which consist of bundles of 10–100 muscle
fibres surrounded by the perimysium, another
connective tissue sheath. The muscle fibres are surrounded by a further layer of connective tissue, the
endomysium. The number of fibres comprising a
whole muscle varies; for example, the medial head
33
34
muscle action in sport and exercise
of the gastrocnemius comprises over one million
fibres, whilst the finger muscle, the first dorsal
interosseous, comprises around 40 000 (Feinstein
et al. 1955). Typically a muscle fibre is approximately 50 µm in diameter, but will be smaller during
infancy, and larger if adaptations have been made,
for example due to strength training. Closer inspection of the muscle fibres reveals that they are in turn
composed of myofibrils all organized side by side.
The myofibrils are strings of sarcomeres arranged in
series, with the sarcomere being the functional unit
where the generation of muscle force takes place. A
typical muscle fibre will be composed of as many
as 8000 myofibrils. Figure 3.1 illustrates the hierarchical structure of muscle. The figure shows that
muscle is composed of a large number of sarcomeres bundled together to form a whole muscle.
In bundling together these sarcomeres there are
significant amounts of connective tissue.
The sarcomere contains two major sets of contractile proteins, the thick myosin filaments and the thin
actin filaments. It is the active interdigitation of
these thick and thin filaments which is responsible
for the generation of force. In experiments performed in the 1960s it was shown how the degree of
overlap between these thick and thin filaments corresponded with the amount of force the sarcomere
could produce under isometric conditions (Gordon
et al. 1966). In these experiments small sections of
muscle were held at a fixed length and stimulated,
the degree of overlap between the filaments was
measured as was the amount of force produced,
then the length was changed and the process
repeated. Figure 3.2 shows the isometric force–
length properties of the sarcomere of frog skeletal
muscle. More sophisticated experimental work by
Edman and Reggiani (1987) has shown that the
curve is much smoother than at first thought,
with a much less defined plateau. Despite these
deficiencies the original curve helps to explain
the phenomena associated with the generation of
muscle forces.
The production of force by muscle can be
explained by the cross-bridge theory. Whilst this is
only a theory it is the one most commonly accepted
by muscle physiologists. The theory is that the force
is due to the formation of myosin cross-bridges connecting with the binding sites on the actin filaments.
The amount of force produced is proportional to the
number of cross-bridges formed (Huxley 1957). As
can be seen in Fig. 3.2 the maximum isometric force
occurs when sarcomere lengths are in their midrange. This length is called the optimum length and
corresponds with the length at which the maximum
number of cross-bridges can be formed. For frog
muscle the optimum sarcomere length is between
2.00 and 2.25 µm (Gordon et al. 1966), whilst for
human muscle it is slightly longer, between 2.60 and
2.80 µm (Walker & Schrodt 1973). At the shorter
lengths the actin filaments from one side overlap
with those from the other side, thus interfering with
the formation of cross-bridges. As the amount of
overlap is increased, from these short lengths, more
cross-bridges can form so force is increased until the
plateau region is reached where the maximum force
is produced. Beyond the plateau region the force
produced by the sarcomere decreases with increasing length because fewer cross-bridges can be formed.
At the upper extreme of sarcomere lengths there is
no overlap between the actin and myosin filaments
and no force can be produced.
Although it is a tedious process, a number of
researchers have taken whole human muscle and
measured the number of sarcomeres comprising the
length of the muscle. From these data it is possible to
infer the properties of whole muscle. From the analysis of eight human cadavers, Huijing (1985) estimated that on average nearly 18 000 sarcomeres are
arranged in series in the myofibrils of the medial
head of the gastrocnemius. Meijer et al. (1998), taking measures from two cadavers, estimated that
on average over 41 000 sarcomeres make up the
myofibrils of the vastus medialis. Many myofibrils
make up a whole muscle and they will not all contain precisely the same number of sarcomeres; there
will be a range, which will affect the properties of
whole muscle. Based on the data in Meijer et al.
(1998) it is possible to examine the force–length
profile of a whole muscle made up of 1000 myofibrils with a mean of 41 800 sarcomeres making
up each myofibril and a standard deviation of 5300
sarcomeres. Figure 3.3 shows the shape of the
muscle-tendon architecture
Whole
muscle-tendon
complex
Tendon
Muscle
Muscle fibre
Connective
tissue
Muscle fibre
Dark
A band
Light
I band
Myofibril
Section
of a myofibril
Z disc
A band
Actin: Thin filament
Myosin: Thick filament
Cross-bridges
Fig. 3.1 The organization of skeletal muscle.
I band
A band
I band
Sarcomere
Z disc
35
36
muscle action in sport and exercise
3.7
(1)
2.2
(2)
2.0
(3)
1.6
(4)
3
2
1
Normalized force
4
1.5
2.0
2.5
3.0
4.0
3.5
Sarcomere length (µm)
Fig. 3.2 The isometric force–length properties of the
sarcomere of frog skeletal muscle, with examples of
sarcomere overlap. (Based on data in Gordon et al. 1966.)
110
force–length curve for this theoretical muscle. The
first thing to note is that variation in the number of
sarcomeres in series gives a muscle with an active
range from 6.5 cm to 21 cm, which is typical of the
lengths we expect from the vastus medialis. The
active range is much broader than it would be for
the uniform number of sarcomeres; this is because
some myofibrils will have their peak at shorter
lengths and others at longer lengths. The optimum
length of this muscle is around 12 cm.
The preceding analysis has assumed that muscles
are arranged in bundles which transmit force along
their length to the end regions, where they attach
to tendon. Muscles often taper at the ends, which
would mean that certain fibres would have to be
longer than others; this constraint would accentuate the effects shown in Fig. 3.3. Loeb et al. (1987)
examined the cat sartorius and showed that not all
muscle fibres ran from one tendon plate to another.
This arrangement has implications for the force–
length properties of whole muscle, also it makes
more complex the mechanism for force transmission to the external tendon. Such an arrangement
has not been demonstrated in human muscle but
may exist.
If, for a given activity, the production of maximum force from a muscle is desired then it makes
sense that when performing the activity the muscle’s range of motion should occur around the
Variation in number of sarcomeres
No variation in number of sarcomeres
100
% Maximum isometric force
90
80
70
60
50
40
30
20
10
0
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Muscle fibre length (m)
0.2
0.22
0.24
Fig. 3.3 The isometric force–length
properties of a muscle composed of
1000 myofibrils with a mean of 41 800
sarcomeres making up each myofibril
and a standard deviation of 5300.
(Values based on data in Meijer et al.
1998.)
muscle-tendon architecture
150
% Maximum isometric force
muscle’s optimum length. Invasive studies on the
semimembranosus of Rana pipiens (a species of
frog), have shown that during the leaping motion
this muscle operates near its optimum length
throughout the movement (Lutz & Rome 1994). This
example from the frog is not a general functional
adaptation of muscle. In vivo measures have been
made on the degree of sarcomere overlap of the
human extensor carpi radialis longus, a wrist extensor muscle, and show that this muscle works on the
descending limb of the force–length curve (Lieber
et al. 1994). In a study of elite runners and cyclists
it was found that the rectus femoris, over its active
range in vivo, was operating on the descending limb
for the runners and the ascending limb for the
cyclists (Herzog et al. 1991). It is possible that these
are self-selected groups, for example that success
comes for the cyclist with a rectus femoris which
works predominantly on the ascending limb of
the force–length curve. It is more likely, though,
that these are functional adaptations caused by
changing the number of sarcomeres in series.
There is evidence in animal studies that such
adaptations can occur; for example, rats made to
run downhill showed increased numbers of sarcomeres in their vastus intermedius (Lynn & Morgan
1994).
As the velocity of a muscle changes so does the
force that muscle can produce, as illustrated in
Fig. 3.4. This relationship was experimentally first
quantified by Fenn and Marsh (1935), and the classic
study was performed a few years later by A.V. Hill
(Hill 1938). Hill’s study was performed using whole
frog sartorius muscle and investigated the variation
in force production at different shortening velocities. More recent work has shown that single muscle
fibres do not produce the same curve as Hill
obtained, with a deviation for the high force/low
speed part of the relationship (Edman et al. 1976). To
understand the force–velocity properties of muscle
fibres it is necessary to define a few terms. A stimulated muscle which shortens is performing a
concentric contraction. If the ends of the muscle
are constrained in some way so that the distance
between the ends is fixed, then a stimulated muscle
is performing an isometric contraction. If a force is
applied to a stimulated muscle which exceeds its
37
100
50
0
–100 –80 –60 –40 –20
0
20
40
60
80
100
Muscle fibre velocity (% maximum)
Fig. 3.4 The force–velocity curve for muscle (positive
velocities—concentric phase, negative velocities—
eccentric phase).
capacity for generating an isometric force then that
muscle will lengthen, and this is called an eccentric
contraction. By convention, concentric contractions
are given positive velocities, whilst eccentric contractions have negative velocities. As the velocity of
a concentric contraction increases, the force the
fibres can produce decreases. As the magnitude of
the velocity increases during eccentric contractions
the force the fibres can produce increases. Some
authors object to the use of the term contraction,
when discussing eccentric activity. This is because
there is no evidence of anything contracting, the
muscle actually lengthens, and muscle volume
remains constant (Baskin & Paolini 1967).
The maximum velocity of shortening is obtained
during the concentric phase; this happens under
the no-load or zero-force condition. Such a velocity
of shortening is not likely to occur in vivo because
a no-load condition is difficult to achieve as the
muscle has to contend with the inertia of the limbs
to which it is connected. The force that can be
produced falls rapidly as velocity increases—a
phenomenon familiar to athletes, who generally
cannot move heavier objects with as high a velocity
as lighter ones.
38
muscle action in sport and exercise
100
Muscle force (% maximum)
90
80
70
60
50
40
30
20
10
0
20
40
60
80
Muscle velocity (% maximum)
100
0
20
40
60
80
100
Muscle length (% maximum)
Katz (1939) performed some of the earliest studies
of eccentrically contracting muscle, and noted that
the forces are higher during the eccentric phase
compared with the concentric phase. Eccentric
contractions only occur when muscle is yielding
to a force. For example, our muscles often work
eccentrically when controlling the landing from
a drop. During many weight training exercises
the major muscle groups work concentrically to
raise the weight and eccentrically to lower it. The
basic force–velocity properties of muscles immediately inform us that lowering the weight should
be, and feel, easier than raising it. Weight trainers
often find they can continue to lower weights
which they can no longer raise. Such lowering of
a weight after failing to raise the weight emphasizes the muscles working eccentrically and is
often referred to as ‘negatives’, which is correct
since if the muscles are lengthening the muscle fibre
velocity will be negative. The eccentric phase of the
force–velocity curve produces the highest muscle
forces, unfortunately few experiments have been
performed precisely to quantify this force, but
estimates range from 110 to 180% of the maximum
isometric force (e.g. Katz 1939; Joyce & Rack 1969;
Mashima 1984).
Fig. 3.5 The force–length–velocity
curve for an idealized muscle; only
the concentric phase of the force–
velocity curve is represented.
The force–velocity properties of muscle can be
explained using cross-bridge theory (Huxley 1957).
The maximum velocity of shortening appears to
be related to the maximum rate at which the
cross-bridges can cycle (Barany 1967; Edman et al.
1988). If this is the case then maximum rate of
shortening would not be affected by the degree
of overlap of the sarcomeres, and therefore the
force–length properties. Edman (1979) has shown
this to be the case.
It would be incorrect to consider the force–length
and force–velocity properties of muscles in isolation because during many movements the length
and velocity of the muscle change simultaneously.
Figure 3.5 illustrates the force–length–velocity properties of an idealized muscle. It should also be
pointed out that this is the curve for a maximally
activated muscle, and there are many other values
obtainable for the muscle forces by varying the
degree of muscle activation.
Muscle fibre organization
The next question to ask is how are the properties of
a muscle affected by their muscle fibre organization
or architecture. The main variations in muscle fibre
muscle-tendon architecture
architecture relate to the number of sarcomeres in
parallel and the number in series. Rather than discuss this aspect of architecture in terms of sarcomeres we will focus on muscle fibres. If we arrange
more muscle fibres in parallel then they can produce
more force, with muscle force being directly proportional to muscle cross-sectional area. Intuitively we
expect such a relationship as individuals with larger
muscles are assumed to be stronger, i.e. capable of
producing more muscular force than others, but we
can also have muscle fibres of different lengths.
Longer muscle fibres have more sarcomeres in
series and so have a larger range of motion. They
can produce force for a greater range of muscle
lengths. They will not be able to produce muscle
forces at as short a length as a short muscle, but will
have a much greater operating range. This is not the
only property which is enhanced for longer muscles
—they can also shorten at higher velocities. Each
sarcomere can shorten at a given rate and the
shortening rate of a fibre will be a direct function
of the number of these in series.
To illustrate the effects of muscle fibre organization, Fig. 3.6 shows the properties of two hypothetical muscles. Both muscles have the same
volume, so they have the same amount of contractile
machinery, but in one the muscle is relatively
long and thin whilst the other is short and thick.
Note that for both muscles the contraction time
will be the same as this does not vary with muscle
size. The peak isometric force is greater for muscle
B, but it has half the working range of muscle A.
Muscle A is able to shorten at twice the maximum
velocity of muscle B due to its greater length, but
muscle B can generate greater amounts of force
for the lower contraction velocities. Power production, particularly peak power, is strongly correlated
with performance in dynamic athletic activities. The
power produced by a muscle is the product of the
force it is producing and the velocity of contraction,
and Fig. 3.6 shows that both muscles produce the
same peak power. Muscle A due to its greater peak
velocity produces peak power at a higher velocity
than muscle B.
Human muscle fibres differ in their precise properties. Basically there are two types, fast (type II)
39
and slow (type I), although these can be divided up
into more detailed subcategories. Fast fibres can
contract quickly and have the enzymes which make
them specialized for anaerobic glycolysis. Slow
fibres contract more slowly and are specialized for
prolonged or sustained activities obtaining energy
via aerobic glycolysis. Human muscle is not homogeneous in terms of fibre type content, so the relative distribution of the fibre types in a muscle helps
determine its properties. In the preceding example
it was assumed that both muscles had the same
muscle fibre types. There is conflicting evidence as
to whether the different fibre types can produce different maximum forces per unit of cross-sectional
area, but the current balance of evidence suggests
that there is no difference. The curvature of the
force–velocity curve does depend on fibre type
(Faulkner et al. 1986), with greater concavity for the
slow fibres (see Fig. 3.7). This greater concavity will
result in reduced force production particularly in
the mid-range of the muscle’s range of shortening
velocities. The maximum shortening velocity of
human muscle has been measured to be 6 fl · s−1
(fibre lengths per second) for type II fibres, and
2 fl · s–1 for type I fibres (Faulkner et al. 1986). The
ratio of these velocities corresponds well with studies on the properties of different fibre types in other
animals (e.g. Close 1964). Figure 3.7 illustrates the
force–velocity curve for three hypothetical muscles,
all of the same length and cross-sectional area:
one muscle is composed of 100% slow fibres and
the other two are 100% fast fibres. Peak force is
the same for all three muscles, but the maximum
velocity of shortening is three times greater for
the ‘fast’ muscles compared with the slow muscle.
This reflects the normal case where fast fibres can
shorten at much higher velocities than slow fibres.
The difference in concavity of the force–velocity
curve also has a significant effect on the forceproducing capabilities of the muscle. To illustrate
this in Fig. 3.7 fast muscle II has been given the
same concavity in its force–velocity properties as
slow fibres. Fast muscle II produces less force
for a given velocity of shortening than fast muscle I, even if it has the same maximum shortening
velocity.
40
muscle action in sport and exercise
Length
Hypothetical muscle A
Hypothetical muscle B
2 units
1 unit
2
Cross-sectional area
2 units2
1 unit
Force–length properties of muscles A and B
Muscle A
2
Muscle B
Muscle A
Muscle B
Muscle force
1.5
1
0.5
0
0.5
1
2
1.5
Muscle fibre length
Force–velocity properties of muscles A and B
2
Power–velocity properties of muscles A and B
0.7
Muscle A
Muscle B
Muscle power
1.5
Muscle force
Muscle A
Muscle B
0.6
1
0.5
0.4
0.3
0.2
0.5
0.1
0
1
2
3
4
6
5
0
1
Muscle fibre velocity
2
3
4
5
Muscle fibre velocity
Key functional properties summary
Contraction time
Maximum force
Range of motion
Maximum velocity
Peak power
Hypothetical muscle A
Hypothetical muscle B
1
1
2
2
2
1
2
1
1
2
Fig. 3.6 The influence of the arrangement of muscle fibres on the force–length, force–velocity, and velocity–power
properties of two hypothetical muscles.
6
muscle-tendon architecture
100
Fast muscle
Concave fast muscle
Slow muscle
Muscle force (% maximum)
90
80
70
60
50
40
30
20
10
0
0.5
1
1.5
2
2.5
3
Muscle fibre velocity (units·s–1)
Fig. 3.7 The concentric phase of the force–velocity curve
for three muscles. These muscles are equivalent in their
properties, except in their fibre type distributions.
Connective tissue
In examining the structure of whole muscle (see
above), it was seen that there are significant amounts
of connective tissue in muscle (fascia, epimysium,
perimysium, endomysium). The component of this
connective material which dictates its properties
is collagen, although there is also some elastin. Both
materials have important elastic properties. As
well as holding everything together, the connective
tissue also provides the framework within which
41
muscle fibres form, and acts as the ducting through
which blood vessels and nerves run. Forces produced by the muscle fibres are, in part, conveyed
through this connective tissue (Street & Ramey
1965), and it has important properties which influence the force output of muscle. If this connective
tissue is thought of as an elastic band acting in
parallel to the contractile machinery, at certain
lengths the contractile machinery will produce
force and the band will be slack, but as the length of
the contractile machinery increases the band will
eventually become taut and also exert a force. At
extreme lengths, the forces caused by the connective
tissue will stop overextension of the muscle fibres
(Purslow 1989). The properties of the connective
tissue are not purely elastic; the force they produce
also depends on the velocity at which they change
length. However, the elastic band analogy stresses
an important feature, namely that at a certain point
in the force–length curve of muscle the connective
tissue is stretched to longer than its resting length
and produces a force.
In Fig. 3.8 the force–length curve is demonstrated
for two different muscles. Each of the muscles starts
to produce force from the parallel elastic component
at a different point in the force–length curve, indicating different relative resting lengths of the parallel elastic component in each of the muscles. The
amount of force produced as the parallel elastic
component is extended beyond its resting length is
Total
% Maximum isometric force
Active
force
Passive
force
Length
% Maximum isometric force
100
100
Total
Active
force
Passive
force
Length
Fig. 3.8 The force–length curve of two muscles with different parallel elastic component contributions to the force output
of the muscle. (Adapted from Wilkie 1968.)
muscle action in sport and exercise
different for each muscle depending on the parallel elastic component’s resting length. In whole
muscles the contributions to force from the parallel
elastic component will vary and will be a function of
the amount of connective tissue in each muscle—the
greater the amount of tissue the larger the forces.
If a limb is forced to rotate about a joint but with
no muscular activity of the muscles crossing the
joint, there will still be a resistance to that motion
caused by the passive structures crossing that joint.
This passive resistance to motion has been assessed
for most human joints (e.g. Hayes & Hatze 1977;
Siegler et al. 1984; Engin & Chen 1986; Vrahas et al.
1990) and is largest towards either extreme of the
joint’s range of motion. Johns and Wright (1962)
examined the sources of this resistance to passive
motion in the wrist of the cat. Their analysis showed
that in the mid-range of movement 51% of the
resistance was caused by the muscle-tendon complexes crossing the joint, while the joint capsule
was responsible for the majority of the remainder
of the resistance (47%). Assuming similar ratios in
humans, the passive properties of muscle contribute
significantly to the passive moment profile at joints.
This passive moment can provide an important contribution to human movement. To activate muscle
takes time as the appropriate signals are sent to the
muscles to produce force, and even when the signal
reaches the muscle the generation of force is not
instantaneous. During an unexpected perturbation
there is a delay before the muscles respond appropriately to resist the externally caused motion. The
parallel elastic components do not require nervous
activation to produce force, and are present before
the muscles can respond. These passive forces can
help to halt unwanted joint extension in contact
sports when the body experiences an unexpected
impact, especially in view of the fact that these
forces are largest at the extremes of a joint’s range
of motion.
The forces muscle fibres generate are applied to
the skeletal system via tendon. Tendon consists predominantly of the protein collagen. Harkness (1961)
examined the Achilles tendon of man, and found
it to be composed of 86% collagen. When viewed
under a light microscope tendons have a crimped
wavelike appearance. Dale and Baer (1974) showed
that this crimping (actually in the collagen) unfolds
during the initial loading of the tendon. Tendon is
not uniform along its whole length; for example, the
insertion onto the bone is a gradual transition from
tendon to fibrocartilage. The tendon is anchored
onto the bone by fibres from the periosteum of the
bone (Cooper & Misol 1970).
The properties of tendon are normally examined
by applying a certain stress (force per unit area) and
measuring the strain (deformation of the material),
then repeating the procedure for a range of stresses.
Such measures tell us that tendon typically breaks at
a strain of 0.08– 0.10, i.e. when it is stretched to a
length 8–10% greater than its resting length (Rigby
et al. 1959; Bennet et al. 1986). For a particular strip of
tendon connected to a muscle, it is simpler to look at
the force the muscle produces and the amount of
extension in the tendon this produces, rather than
considering stress–strain relationships. Figure 3.9
shows the force–extension curve for a strip of tendon, with the amount of extension of the tendon
increasing with increasing force. The low force end
of the curve is the so called ‘toe’ region; here small
amounts of force cause the uncrimping of the collagen. This phase of tendon loading causes relatively
large amounts of tendon extension. The curve
shows both the loading and unloading of the tendon; these two curves do not overlie one another,
but demonstrate a hysteresis. This means that not all
of the energy stored in the tendon during loading
is returned during unloading. The gap between the
Force
42
Extension
Fig. 3.9 The force–extension curve of a tendon. The
arrows reflect the direction of loading and unloading.
muscle-tendon architecture
two curves indicates the efficiency of tendon as an
energy store. For a variety of mammalian tendons
the energy loss is between 6% and 11%, indicating it
is a very efficient energy store (Bennet et al. 1986).
The tuning of the properties of tendon to the contractile element with which it lies in series has an
important impact on human movement (see ‘Interactions in the muscle-tendon complex’ below).
The myofibrils in series and parallel comprise the
contractile component of the muscle-tendon complex. Tendon is often referred to as a series elastic
component because it is an elastic material which
lies in series with the contractile component. However, in a muscle the line of action of the muscle
fibres is not always coincident with that of the
tendon. These elastic properties have important
implications for the in vivo performance of skeletal
muscle.
As well as tendon external to the muscle belly
there may also be significant amounts of tendon
inside the muscle belly (aponeurotic tendon). The
properties of the external and internal tendon are
the same (Proske & Morgan 1987). The amount of
such tendon depends on the relative arrangement of
the muscle fibres and tendon, and this is discussed
in the following section.
Muscle pennation
In many human skeletal muscles the fibres may be
orientated at an angle to the tendon external to
the muscle belly. The angle between the tendon
and muscle fibres is called the pennation angle
(Fig. 3.10). If the pennation angle is zero then the
muscle is said to be parallel fibred or fusiform.
There are a variety of types of muscle pennation:
principal among these are unipennate, where all
the fibres are aligned in one direction, and bipennate, where they are aligned in two directions.
Muscle pennation angles vary between individuals.
Wickiewicz et al. (1983) dissected three cadavers and
reported different pennation angles for the same
muscle. For example, the vastus intermedius in two
of the cadavers had a pennation angle of 5° whilst in
the other the angle was 0° (it was parallel fibred).
Table 3.1 shows the ranges of angle of pennation for
some human muscles.
43
Parallel
(a)
Unipennate
α
(b)
Bipennate
(c)
Complex unipennate
(d)
Fig. 3.10 Illustration of different organization of muscle
and tendon, including parallel fibred (fusiform),
unipennate and bipennate. The angle describing the
orientation between the external tendon and muscle fibres
is α, the angle of pennation.
The maximum isometric force a muscle belly can
produce is a direct function of the number of
myofilaments in parallel with one another. If the
cross-sectional area (CSA) of a muscle is measured
in the plane perpendicular to the long axis of the
limb, then for a parallel fibred muscle the force in
the tendon is equal to the muscle fibre force and is
directly proportional to the cross-sectional area. For
a pennated muscle the same relationship does not
hold, and account must be taken of the angle of
Table 3.1 The ranges of muscle pennation reported for
some human muscles. (Data from Yamaguchi et al. 1990.)
Muscle
Gluteus maximus
Gluteus medius
Gluteus minimus
Biceps femoris
Gastrocnemius medialis
Gastrocnemius lateralis
Pennation angle (deg.)
3.4–5
8.0–19.0
5.0–21.0
7.0–17.0
6.5–25.0
8.0–16.0
44
muscle action in sport and exercise
pennation. For a pennated muscle the following
relationship can be stated:
FT = FF cos(α) ∝ cos(α) × PCSA
(3.1)
where FT is the force in tendon, FF is the force
produced by the muscle fibres, α is the angle of
pennation, and PCSA is the muscle’s physiological
cross-sectional area. (Note the symbol ∝ means proportional to.) To allow for the pennation angle the
concept of physiological cross-sectional area (PCSA)
has been introduced. In essence the PCSA is the
cross-sectional area of the muscle measured in a
plane perpendicular to the line of action of the
muscle fibres. For a parallel fibred muscle the
following is true:
FT ∝ CSA (CSA = PCSA)
(3.2)
whilst for a pennated muscle:
FT ∝ PCSA (CSA < PCSA)
(3.3)
With cadavers the PSCA of a muscle can be measured by a variety of means. In vivo medical imaging
techniques (e.g. magnetic resonance imaging) can
be used to estimate PSCA, usually by taking serial
images of the muscle along its length and from these
measuring the muscle volume, and then applying
the following formula:
PCSA =
Volume cos(α)
FL
(3.4)
where FL is the fibre length (e.g. Fukunaga et al.
1996). For a number of human muscles the PCSA
has been measured, and such data permit an evaluation of the individual muscles’ potential contributions at a joint. Table 3.2 shows both the CSA and the
PCSA of the major ankle plantarflexors—the larger
the PCSA the greater the maximum force the muscle
can produce.
If the muscle fibres are orientated at an angle α to
the tendon then the force in the tendon, which is the
same force that is transmitted to the skeletal system,
is obtained from
FT = FF cos(α)
Table 3.2 The cross-sectional (CSA) and physiological
cross-sectional (PCSA) areas of major human ankle
plantarflexors. (Mean data from Fukunaga et al. 1992.)
(3.5)
The cosine of zero is one, so for a parallel fibred
muscle all of the force is transmitted to the tendon.
With increasing angles of pennation the cosine term
Muscle
Medial gastrocnemius
Lateral gastrocnemius
Soleus
Flexor hallucis longus
Tibialis posterior
Flexor digitorum longus
CSA (cm2)
PCSA (cm2)
16.49
11.24
29.97
4.85
5.40
1.59
68.34
27.78
230.02
19.32
36.83
9.12
decreases (e.g. cos(10) = 0.98, cos(20) = 0.94, cos(30)
= 0.87) so less force is transmitted to the tendon.
Therefore, pennation has an immediate effect on
the output of the muscle fibres. For a given force
produced by the muscle fibres, less is transmitted to
the external tendon. A change in fibre length also
results in less change in the muscle belly length, and
the velocity of shortening of the muscle fibre length
is less than that of the whole muscle belly. The
advantage of pennation is that it allows the packing
of a large number of fibres into a smaller crosssectional area. Figure 3.11 illustrates two muscles,
both with the same number of fibres of the same
thickness, one parallel fibred and the other with a
pennation angle of 30°. The parallel fibred muscle is
thicker than the pennated muscle, so by increasing
the pennation angle, with all other factors being
equal, thickness of the muscle belly decreases.
The degree of muscle pennation changes the way
muscular mass is distributed along the length of a
limb. The pennated arrangement can allow more of
the muscle mass to be closer to the joint, compared
with the distribution for parallel fibred muscles.
This distribution of the muscular mass reduces the
segmental moment of inertia about axes of rotation
passing through the joint, corresponding to a reduction in the limb’s resistance to rotation. Table 3.2
illustrates that the muscles associated with the
shank are pennated, thus focusing more muscular
mass nearer the proximal joint axes of rotation of the
limb than would be achieved if the muscles were all
parallel fibred.
Examination of different muscles in terms of their
length, pennation and PCSA gives insight into their
muscle-tendon architecture
Parallel fibred
45
Unipennate
t
α
LB and
LF
LB
t
Fig. 3.11 The influence of pennation
angle on the thickness of muscle.
CSA, cross-sectional area; PSCA,
physiological cross-sectional area.
LF
α= 0°
CSA= 10 cm2
PSCA= 10 cm2
Volume = 100 cm3
t= 10 cm
LF = 10 cm
LB = 10 cm
role. For example, the human soleus has relatively
high pennation angles, short fibres, and a large
cross-sectional area, which means it is well designed
to produce large forces. In contrast, the gastrocnemius has longer fibres, a smaller angle of pennation,
and a smaller cross-sectional area. In comparison to
the soleus the gastrocnemius can produce lower
forces but can operate over a greater range and
at higher velocities of shortening. Support for the
implied functional adaptations of these muscles
comes from the data of Johnson et al. (1973) who
examined the fibre type distribution in these
muscles and found the soleus to be composed of
predominantly type I (slow) fibres, and both
heads of the gastrocnemius to have a homogeneous distribution with equal amounts of type I and
type II (fast) fibres.
This architectural property of muscle is not as
simple as presented because as a pennated muscle
shortens the pennation angle changes. Herbert
and Gandevia (1995) used computerized sonography to measure the pennation angle of the human
brachialis (an elbow flexor). Their results show that
α = 30°
CSA= 5 cm2
PSCA= 10 cm2
Volume = 100 cm3
t= 5 cm2
LF = 10 cm
LB = 24.33 cm
as the muscle shortens its pennation angle increases,
in this case from around 9° to 25°. Muscle shortening will occur as muscle fibres shorten to generate
force. In addition, as a joint angle reduces from
full extension the muscle-tendon complex generally
needs to be shorter to be able to actively apply forces
to the skeleton, therefore with decreasing joint angle
the muscle fibres have to be shorter in order to
reduce muscle-tendon complex length. Hence, with
muscle shortening, pennation angle increases which
in turn means that there is a concomitant change
in transfer from the muscle fibres to the external
tendon.
With strength training one of the adaptations of
muscle is additional muscular mass caused by the
fibres becoming thicker (hypertrophy). If a muscle
hypertrophies then it would be anticipated that this
would be accompanied by the muscle becoming
thicker. If great increases in muscle thickness are to
be avoided this can be achieved by simultaneously
increasing muscle pennation angle. The muscle
fibres can become larger but with an increase in
pennation angle there need not be a concomitant
46
muscle action in sport and exercise
increase in muscle thickness. Kawakami et al. (1993)
used ultrasound to measure changes in pennation
angle in the human triceps brachii due to strength
training. Their results showed a clear increase in
pennation angle with strength training. Considering that increasing pennation angle reduces the
output from the muscle fibres to the tendon there
must be subtle trade-offs occurring when increased
pennation is part of the adaptation associated with
increased strength.
The representation of muscle architecture
shown in Fig. 3.11 serves to illustrate how the key
properties of muscle are influenced by pennation.
Van Leeuwen and Spoor (1992) demonstrated that
the orientation of muscle fibres and aponeurosis
as shown in Fig. 3.10 creates muscles which are
mechanically unstable. Muscle fibres in pennated
muscle do not necessarily run in straight lines and
can have curved paths, and the aponeurosis can
also be curved. Van Leeuwen and Spoor (1992)
identified in the human gastrocnemius curvature of
both the muscle fibre paths and the aponeurosis.
More realistic representations of muscle pennation
therefore have the aponeuroses at an angle to the
external tendon (e.g. Fig. 3.10d), and allow for
curved muscle fibres and aponeuroses. A complete
understanding of muscle in vivo will require greater
investigation of these phenomena.
Interactions in the muscle-tendon
complex
When examining how muscles produce moments
at the joints it is important to consider the role of
the whole muscle-tendon complex. The forces pro-
duced by the muscle fibres are transmitted to the
skeleton via tendon. The resulting changes in joint
angles and angular velocities will depend on the
length and velocity of the muscle-tendon complex
(see next section). As tendon is an elastic material,
its length changes as forces are applied to it. Tendon
compliance has a significant effect on the properties
and functioning of the muscle-tendon complex.
As a preliminary illustration of the role of the
elastic tendon consider a muscle-tendon complex
whose ends are fixed (see Fig. 3.12). As the muscle
fibres shorten to generate more force the tendon
stretches (albeit somewhat exaggerated in the figure). Therefore, under isometric conditions, where
the length of the muscle-tendon complex does not
change, the tendon actually lengthens whilst the
muscle fibres shorten. The length of the muscletendon complex is the sum of the length of the
fibres and the length of the external tendon for
parallel fibred muscles (similar relationships exist
for pennated muscles). This implies that in vivo joint
angle changes can be achieved by shortening of
muscle fibres and lengthening of the tendon. The
force–length properties of the muscle-tendon complex are not therefore the same as those of the
fibres. The muscle-tendon velocity can be represented by the following equation:
VMT = VF + VT
(3.6)
where VMT is the velocity of the muscle-tendon complex, VF is the velocity of the muscle fibres, and VT is
the velocity of the tendon. So as the muscle-tendon
complex contracts, its velocity is equal to the sum of
the tendon and muscle fibre velocities, where these
two latter quantities need not be equal. Indeed, the
No force
Low force
High force
Fig. 3.12 The extension of tendon
and shortening of the muscle fibres
during an isometric muscle action.
muscle-tendon architecture
elasticity of tendon means that it is unusual for tendon and fibre to have the same velocities. In the following paragraphs the extent to which tendon may
lengthen is discussed, as well as the influence of this
lengthening on muscle-tendon complex properties.
The analysis of these properties and those presented
to date are for parallel fibred muscles, although the
same principles apply with little modification to
pennated muscles.
Human tendon is not very compliant, snapping once stretched to 10% of its resting length.
Measurements made in vivo in humans and other
animals typically report that tendon is stretched
between 2 and 5% by the maximum isometric force
of its muscle fibres (e.g. Morgan et al. 1978; Woittiez
et al. 1984; Bobbert et al. 1986a; Loren & Lieber 1995).
The maximum forces a tendon will experience will
be greater than the maximum isometric force
because maximum forces are larger under eccentric
conditions, but even so the stretching of tendon seen
in vivo leaves a significant safety margin between
peak strain and breaking strain. Muscles vary in the
length of their external tendon, which means they
vary in the extent to which the whole muscletendon complex length is influenced by tendon
extension. To understand these variations it is
useful to compare muscles in terms of the ratio of
their external tendon length to muscle fibre length.
In equation form:
ratio 1 =
LTR
LF,OPTIM
(3.7)
where LTR is the resting length of the external tendon, and LF,OPTIM is the length of the muscle fibres at
their optimum length. If the tendon strain due to the
maximum force produced by the fibres is the same
for all muscles, then the higher this ratio the greater
the contribution of tendon stretch to overall muscletendon length. In other words, the longer the tendon
relative to the muscle fibres the more influence the
tendon properties will have. Human muscles typically have ratio-1 values greater than one, indicating
that the tendon is longer than the muscle fibres.
Figure 3.13 shows four theoretical muscles and the
influence of variations in tendon length, fibre length
and maximum tendon extension under maximum
isometric muscle force on the force–length proper-
47
ties of the whole muscle-tendon complex. Increasing both tendon extension and tendon length causes
a shift of the force–length curve of the whole muscle-tendon complex to the left compared with the
curves for the inelastic tendon, therefore increasing
the operating range of the muscle-tendon complex.
For pennated muscle the length of the muscle belly
is the important factor dictating whole muscletendon complex force–length curves, but the principles presented still apply.
The stress applied to a tendon is directly proportional to the muscle PCSA, and the strain the
tendon experiences is directly proportional to the
tendon cross-sectional area (TCSA). The following
ratio expresses the relationship between the tendon
strain and the muscle stress
ratio 2 =
PCSA
TCSA
(3.8)
Tendon does not generally have a cross-sectional
area as large as the muscle fibres, with ratio-2 values
normally between 10 and 100. The higher this ratio,
the more strain the tendon experiences.
These two ratios provide insight into the functional adaptation of muscle designed to utilize the
properties of tendon. For example, if both ratios are
high then the force produced by the muscle fibres
causes larger stretches in long tendons, which
causes a large change in muscle-tendon complex
length. Conversely, if both ratios are low then the
maximum muscle force does not cause much
change in the length of the tendon, which is short
anyway; therefore tendon extension only causes
small changes in muscle-tendon complex length.
Table 3.3 presents the ratios for a variety of human
muscles. When the ratios are low, the muscle seems
well adapted for fine control since when the fibres
shorten to produce force there is only a modest
change in tendon length. This control of muscletendon length (and therefore joint angle and angular
velocity) does not require detailed allowance for
tendon stretch. For example, the wrist muscles extensor carpi radialis brevis and extensor carpi radialis longus fall into this category. When the ratios
are both high, potential changes in tendon length
are relatively high. It has been argued that such
changes are advantageous in movement because
48
muscle action in sport and exercise
Elastic tendon
Inelastic tendon
Model 2
100
100
80
80
Muscle force
Muscle force
Model 1
60
40
40
20
20
0
70
60
80
90
100
110
120
0
70
130
80
Muscle-tendon complex length
90
110
120
130
Model 4
100
80
80
Muscle force
Muscle force
Model 3
100
60
40
60
40
20
20
0
70
100
Muscle-tendon complex length
80
90
100
110
120
130
0
70
80
90
100
110
120
130
Muscle-tendon complex length
Muscle-tendon complex length
Model 1: resting muscle-tendon length comprises 20%
fibre and 80% tendon. Tendon extension under
maximum isometric force is 0.75%
Model 3: resting muscle-tendon length comprises 80%
fibre and 20% tendon. Tendon extension under
maximum isometric force is 0.75%
Model 2: resting muscle-tendon length comprises 80%
fibre and 20% tendon. Tendon extension under
maximum isometric force is 4.00%
Model 4: resting muscle-tendon length comprises 80%
fibre and 20% tendon. Tendon extension under
maximum isometric force is 4.00%
Fig. 3.13 The force–length properties for four hypothetical muscles compared with equivalent muscles with inelastic
tendons.
the tendon can act as an energy store. Also, changes
in tendon length can allow the muscle fibres to produce more force by enabling them to work for
longer periods closer to their optimum length. The
human gastrocnemius is an example of a muscle
where both ratios are relatively high.
It is methodologically difficult to measure muscle
and tendon length changes in vivo, but Roberts et al.
(1997) successfully did this for running turkeys.
They showed that during the support phase of running the muscle fibres of the turkey’s lateral gastrocnemius remained at the same length whilst the
muscle-tendon architecture
49
Table 3.3 The ratio of tendon length (LTR) to muscle fibre length (LF,OPTIM), and the ratio of muscle physiological crosssectional area (PCSA) to tendon cross-sectional area (TCSA) for some human muscles. (Data extracted from Hoy et al.
1990; Loren & Lieber 1995; Woittiez et al. 1985.)
Muscle
Vastii
Lateral gastrocnemius
Soleus
Hamstrings
Extensor carpi radialis brevis
Extensor carpi radialis longus
Extensor carpi ulnaris
Flexor carpi radialis
Flexor carpi ulnaris
changes in the length of the gastrocnemius muscletendon complex were achieved by the stretching
and recoiling of the tendon. They idealized that the
muscle fibres acted as rigid struts rather than the
active generators of motion. Such an arrangement
makes sense because muscles consume less energy
when they perform isometric contractions compared with concentric contractions (Ma & Zahalak
1991). Eccentric contractions can be less costly than
isometric contractions, but since during a cyclical
activity the muscle fibres would have to shorten and
lengthen, the net energy cost would be higher than
when performing just an isometric contraction.
Alexander et al. (1982) provide an extreme example
of the use of tendon as an elastic energy store. In the
camel the plantaris runs from the femur to the toes,
with a few millimetres of muscle and over one metre
of tendon. Any active changes of length of the muscles will have little effect on overall muscle-tendon
length so these tendons act like springs which
stretch during landing from a stride and recoil during the push-off. In humans, such extreme examples
are hard to find but Alexander (1992) has provided
evidence of how the human Achilles tendon functions in a similar fashion during running. The
ground reaction forces during the support phase of
running are sufficient to stretch the Achilles tendon
to such an extent that the stretch and recoil of the
tendon can account for most of the motion at the
ankle joint during this phase of running.
Ratio 1 =
L TR
LF ,OPTIM
2.68
8.85
11.25
3.60
2.89
2.10
3.67
3.86
4.96
Ratio 2 =
PCSA
TCSA
–
96.3
106.0
–
16.4
9.2
13.4
12.0
13.3
In humans it is particularly hard to measure the
changes in length of the muscle fibres and tendon in
vivo. One way to circumvent these methodological
problems is to use computer models which simulate
the motion of interest and estimate muscle fibre and
tendon behaviour. Bobbert et al. (1986b) simulated
the activity of the triceps surae during maximum
vertical jumping. Their results show that in both the
soleus and gastrocnemius during the final phase of
the jump the tendon had a higher velocity of shortening than the muscle fibres. Therefore, the overall
velocity of the muscle-tendon complex is greater
than that of the muscle fibres. At higher velocities
of shortening, the muscle fibres produce less force
(Fig. 3.4), so allowing the tendon to shorten at a
higher velocity permits the fibres to shorten at a
lower velocity but with greater force. This recoiling of the tendon is hypothesized to occur due
to stretching of the tendon during the countermovement phase of the jump.
The muscle cross-bridges do exhibit a degree of
elasticity (Huxley & Simmons 1971), but this elasticity is less than that of the tendons and is dependent
upon the degree of activity of the fibres and their
length. Alexander and Bennet-Clark (1977) have
demonstrated that as a general principle, if the tendon is longer than the muscle fibres, the tendon is
the predominant site of energy storage.
The aponeurosis in pennated muscle is essentially
the same material as the tendon external to the
50
muscle action in sport and exercise
muscle belly; therefore as the muscle fibres generate
force the aponeurosis is stretched beyond its resting
length. Otten (1988) showed that if the aponeurosis
was assumed to be elastic this caused an increase in
the active range of the force–length properties of the
muscle belly, similar to that illustrated in Fig. 3.13.
The stretching of the aponeurosis may be heterogeneous (Zuurbier et al. 1994), which probably means
that, depending on where they are attached to the
aponeurosis, different fibres in a pennated muscle
could be operating at quite different lengths. It is
also important to consider that the aponeurosis
may be an important energy store like the external
tendon. Such subtleties of muscle-tendon design
have yet to be fully elucidated.
Muscle-tendon line of action
The resultant joint moment is the sum of the
moments caused by the muscles crossing the joint,
the moment caused by articular contact forces, and
the moments due to the ligaments. It is only the
muscular moments which are under direct control
of the nervous system. In the preceding sections, reference has been made to the factors which dictate
muscle forces, but it is also important to consider the
translation of these linear forces to the rotational
moments at the joints. The moment for a given
muscle is the product of the tendon force and the
muscle’s moment arm. The moment arm of a
muscle depends on its line of action relative to the
joint centre of the joint it is crossing. Figure 3.14a
shows how the moment arm of the human biceps
brachii varies with the elbow joint angle. The relationship is not linear and is influenced by a number
of factors including the fact that the joint centre is
not normally in a fixed position but changes as the
bony structures of the joint rotate about each other.
Measurement of the moment arms of a variety of
human muscles, both in cadavers and in vivo, have
shown that they vary in a non-linear fashion with
joint angle. Figure 3.14a demonstrates that even if
the muscle-tendon complex produced the same
forces for all lengths and velocities, there would still
be variation in the moments these forces produce at
the joint because of the muscle’s variable moment
arm.
Table 3.4 presents the maximum isometric force
and the moment arms of the major elbow flexors for
a given joint angle. The brachioradialis can produce less than a third of the force of the biceps
but because of its larger moment arm it can produce two-thirds of the moment. Therefore, a large
moment arm can compensate for a muscle not
Moment arm (cm)
50
40
30
20
10
0
20
40
60
80
100
120
140
Joint angle (degrees)
(a)
Muscle length (cm)
380
360
340
320
300
280
0
(b)
20
40
60
80
Joint angle (degrees)
100
120
140
Fig. 3.14 For the human biceps
brachii (a) the joint angle/muscle
moment arm relationship, and (b) the
joint angle/muscle length
relationship, where 0 degrees is full
elbow extension. (Based on the
equations of Pigeon et al. 1996.)
muscle-tendon architecture
51
Table 3.4 The maximum force, moment arm and maximum moment of the major elbow flexors for a given joint angle.
(Data obtained from the model of Challis and Kerwin 1994.)
Muscle
Biceps brachii
Brachialis
Brachioradialis
Maximum force
(N)
Moment arm
(m)
Maximum moment
(N · m)
600.6
1000.9
262.2
0.036
0.021
0.054
21.6
21.0
14.2
having a large PCSA and therefore low maximum
force-production capacity. Such factors show how it is
important not to consider the properties of a muscletendon complex in isolation of its moment arm.
As a joint angle changes, so must the muscletendon complex length if it is not to become slack;
Fig. 14b shows the change in biceps length with
joint angle. Muscles do not generally run in straight
lines from their origins to their insertions, although
this serves as a good first approximation to their line
of action. To illustrate the influence of the line of
action of a muscle on its properties, two hypothetical muscles are presented in Fig. 3.15. Both muscles
are identical except for the locations of their origins
and insertions. Varying their origins and insertions
changes both the moment arm and muscle-tendon
complex length of each of the muscles for a given
joint angle. This approximation to reality clearly
illustrates how influential this aspect of muscle
architecture is on muscle properties.
To further illustrate the influence of the location
of the origin and insertion of a muscle on the muscle’s potential contribution to the moment at a joint,
the two muscles in Fig. 3.15 are examined for a range
of joint angles; these results are presented in Fig.
3.16. Muscle B has a larger moment arm than muscle
A throughout the range of motion of the joint (Fig.
3.16a). This implies that all other things being equal,
it will be able to produce higher joint moments than
muscle A. The differences in moment arms of the
two muscles also mean that a given change in
muscle length will cause a much smaller change in
joint angle for muscle A compared with muscle B.
Figure 3.16b shows that muscle B is shorter than
muscle A throughout the range of motion. How this
affects the force-producing capacity of a muscle
depends on the muscle’s optimum length. For these
(a) Long moment arm
(b) Long moment arm
2/3 muscle–tendon length
(c) Same muscle length as in (a),
short moment arm
(d) Short moment arm
2/3 muscle–tendon length
Fig. 3.15 Moment arm, muscle length and change in joint
angle.
simulations it was assumed that their optimum
muscle fibre lengths were equal, so for isometric
conditions we obtain the curves in Fig. 3.16c. Note
the peak isometric muscle force is produced at different joint angles for the two muscles due to their
different muscle lengths at the same joint angles.
The moment generated at a joint by a muscle is the
product of the muscle force and moment arm. For
these two muscles the maximum isometric moment
muscle action in sport and exercise
0.08
Muscle A
Muscle B
0.06
0.04
0.02
0
50
(a)
100
150
0.35
Muscle length (cm)
Muscle moment arm (cm)
52
Joint moment (N · m)
Muscle force (N)
600
400
200
50
100
150
200
150
200
40
20
50
100
Joint angle (degrees)
20
Joint moment (N · m)
Muscle velocity (m · s–1)
150
60
(d)
1
0.5
0
100
Joint angle (degrees)
0
200
Joint angle (degrees)
1.5
(e)
50
80
800
0
0.2
(b)
1000
(c)
0.25
0.15
0
200
Joint angle (degrees)
0.03
0.5
1
10
5
0
1.5
Time (s)
15
(f)
0.5
1
1.5
Time (s)
Fig. 3.16 Two theoretical muscles, A and B, have the same properties but different origins and insertions and this gives
muscle B the larger moment arm. (a) Joint angle/muscle moment arm relationship. (b) Joint angle/muscle length
relationship. (c) Joint angle/muscle force relationship under isometric conditions. (d) Joint angle/muscle moment
relationship under isometric conditions. (e) Muscle velocity during joint extension at constant joint angular velocity.
(f) Joint moment during joint extension at constant joint angular velocity.
throughout the joint’s range of motion is shown in
Fig. 3.16d, which illustrates how muscle B produces
the largest joint moment throughout most of the
joint range of motion, because the larger moment
arm of muscle B compensates for its not producing
muscle forces as high as muscle A for much of the
range of motion.
Much of human movement is dynamic, so the two
theoretical muscles were used to simulate an isovelocity joint extension. In these cases the assump-
tion was that the muscles were maximally active
throughout the range of motion and the joint angular velocity was a constant 90° · s–1. Muscle A has the
smaller moment arm, which means that for a given
change in muscle length this produces a larger
change in joint angle than muscle B. Therefore, for
this isovelocity joint extension muscle B, due to
its large moment, has a greater muscle-shortening
velocity throughout the range of motion compared
with muscle A (Fig. 3.16e). The forces produced by
muscle-tendon architecture
these muscles were computed allowing for the
force–length and force–velocity properties of the
muscle fibres, and then their moment was computed by taking the product of their moment arm
and muscle force. Under static conditions, muscle B
could generally produce higher moments than muscle A; but, under these isovelocity conditions this
was not the case as the force–velocity properties
of muscle fibres were also important. When the
moment generated by each of the muscles is computed, the influence of the force–velocity properties
is highlighted. For much of the movement muscle
A produces greater moments than muscle B due
to its lower shortening velocity, despite muscle A
having a smaller moment arm. There are a number
of strength testing and training machines which
endeavour to force a joint to maintain an isovelocity
flexion or extension. These results also demonstrate
that although the joints may be operating at constant velocity the muscles are not.
To summarize the results presented above, the
location of the origin and insertion of a muscle has a
significant effect on the moment-producing capacity
of a muscle. If the moment arms are large, the
muscle generally operates over a shorter range of
motion than a muscle with smaller moment arms.
But a muscle with larger moment arms will have
to shorten at higher velocities than a muscle with
smaller moment arms to produce the same joint
angular velocity. These aspects of a muscle’s properties are crucial and should be considered when
examining the potential role or function of a muscle.
For example, if a muscle has to produce a large
moment at a joint under static or near static conditions it is possible for that muscle to compensate for
not having a large PCSA by having large moment
arms. In contrast, even though a muscle may be composed of predominantly type I fibres (slow), it is possible for a muscle to produce rapid joint extensions by
having a small moment arm. Clearly the design and
specialization of muscle is complex, with a number
of important factors interacting with each other.
Summary
The contractile unit is the sarcomere, with muscle
composed of many strings of sarcomeres. The force
53
a sarcomere produces changes with its length in a
parabolic fashion; it also changes with its velocity
of shortening or lengthening. A shortening muscle
can produce less force with increasing velocity. A
lengthening muscle can produce more force as it
yields to the force being applied to it. In whole muscle the more muscle fibres that are arranged parallel
to one another, the greater the potential for generating force. In whole muscle, pennation allows for
more efficient packing of muscle fibres. If the total
range over which a muscle can produce force or
maximum velocity of shortening is important then
longer muscle fibres are required.
Muscle fibres are connected to the skeletal system
via tendon. Tendon has important influences on
muscle-tendon output. There are two key properties
of tendon which indicate their function: their length
relative to the length of the muscle fibres; and their
cross-sectional area relative to the muscle’s physiological cross-sectional area. There is evidence that
having tendons which are relatively long and thin
makes movement more efficient. In this case the tendon stretch and recoil can permit the muscle fibres
to stay at a constant length, and therefore require
less energy, or to shorten at lower velocities, and
therefore produce greater force. In contrast, it is possible to have muscle-tendon complexes where the
tendon does not exhibit large changes in length
because the tendon is short relative to the muscle
fibres or because the tendon is thick relative to the
muscle fibres, or some combination of both. Such an
adaptation is useful if fine control of movement is
important because muscle length can be controlled
without significant tendon stretch having to be
accounted for.
The origin and insertion of a muscle influences
the moment arm of the muscle about the joint. This
moment arm is important because the forces the
muscle-tendon complex produce are transformed
into rotational moments, with the net moment being
the product of the tendon force and the moment
arm of the muscle. Therefore, muscles with larger
moment arms produce larger moments than other
muscles, all other things being equal. A muscle with
a larger moment arm will have to shorten at higher
velocities than a muscle with smaller moment arms
to produce the same joint angular velocity. So, a
54
muscle action in sport and exercise
muscle with a small moment arm can still produce
large moments because during dynamic movements these muscles have the potential to shorten at
lower velocities than muscles with large moment
arms. Muscles which have fibre type distributions
which indicate specialization for slow contractions
may actually be capable of producing fast joint
movements if the origin and insertion are arranged
to give the muscle a small moment arm.
Most muscles in the human musculoskeletal
system are designed to fulfil a number of different roles, therefore they are not easily classified as
showing one specialization over another. But the
preceding review has highlighted some of the
ways in which muscle-tendon architecture can
influence the forces and moments a muscle can
produce and therefore how they influence athletic
performance.
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Chapter 4
Eccentric Muscle Action in Sport and Exercise
B.I. PRILUTSKY
Definitions of eccentric muscle action
and negative work and power
In sport and exercise, as well as in daily life, people
perform movements by activating skeletal muscles.
Depending on whether active muscles shorten,
stretch or remain at a constant length, three major
types of muscle action can be distinguished: concentric, eccentric and isometric. These three types of
muscle action are often called concentric, eccentric
and isometric contractions. The latter terminology
might be confusing because the word ‘contraction’ has the meaning of shortening. Therefore in
this chapter, the former terminology proposed by
Cavanagh (1988)—concentric, eccentric and isometric muscle actions—is adopted.
A muscle is acting eccentrically if it is active (i.e.
produces active force as opposed to passive force,
see Chapter 2) and its length is increasing in
response to external forces (e.g. weight of load, force
produced by other muscles, etc.). Correspondingly,
muscle is acting concentrically if it is active and
shortens. When the length of active muscle is
prevented from shortening by external forces and
remains constant, the muscle performs isometric
action.
Eccentric muscle action takes place in most
athletic activities. Therefore, it is important to
understand the biomechanical and physiological
consequences of eccentric muscle action and how
it may affect performance.
To characterize eccentric action in athletic movements and its influence on the physiological systems
of the body, a quantitative definition of eccentric
56
action is needed. Consider an isolated muscle with
one end fixed and the other end attached to a
load (Fig. 4.1). Intensity (or the rate) of eccentric
action can be conveniently defined as the product
Pm = Fm × Vm , where Fm is muscle force applied to
the load, Vm is muscle velocity (or the component
of velocity at the point of force application along
the line of muscle action), and Pm is power produced
by muscle force (or muscle power). If force Fm is
smaller than the weight of the load Fe, the load will
be moving in the direction opposite to the exerted
muscle force (i.e. in a negative direction). In this
example, muscle will be performing eccentric action,
and muscle power will be negative (Fig. 4.1a). The
amount of eccentric action can be defined as the
time integral of muscle power Pm, which equals
negative work done by the muscle force, Wm. By
similar methods, the rate and amount of concentric
action can be defined as positive muscle power and
positive muscle work, respectively (the product Fm
× Vm is positive because Vm has the same positive
direction as Fm; Fig. 4.1b). If muscle force does not
produce power and does no work (i.e. the muscle
force is equal to weight of the load and Vm = 0;
Fig. 4.1c), the muscle performs isometric action.
Thus, for quantitative analysis of eccentric action
in athletic activities, muscle forces and velocities
should be recorded. Forces of individual muscles
are typically estimated using mathematical modelling (for reviews, see Crowninshield & Brand 1981;
Hatze 1981; Zatsiorsky & Prilutsky 1993; An et al.
1995; Herzog 1996; Tsirakos et al. 1997), although
direct force measurements from selected muscles
are also possible (Komi 1990; Komi et al. 1996).
eccentric action
Eccentric
action
Concentric
action
Isometric
action
Fm
Fm
Vm
Fm
m
m
m
Vm = 0
Vm
Fe = –9.81m
Fe = –9.81 m
Fe =– 9.81m
Pm =Fm ·Vm <0
Pm =Fm ·Vm >0
Pm =Fm ·Vm = 0
Wm =∫Pm ·dt<0
(a)
Wm =∫Pm ·dt>0
(b)
Wm =∫Pm ·dt= 0
(c)
Fig. 4.1 Definitions of eccentric, concentric and isometric
muscle actions and of negative and positive muscle work.
(a) Eccentric muscle action takes place when force
developed by the muscle, Fm, is smaller than an external
force Fe (in this example, weight of mass m, –9.81 · m) and
the direction of displacement of the point of muscle force
application is opposite to the direction of muscle force
action. The intensity (or rate) of eccentric action is defined
as negative muscle power (Pm = Fm × Vm < 0, where Vm
is the velocity component of the point of muscle force
application along the line of muscle force action). The
integral of Pm over the time of muscle force development
defines the amount of eccentric action or negative muscle
work, Wm < 0. (b) Concentric muscle action takes place
when force developed by the muscle, Fm, exceeds an
external force and the direction of displacement of the
point of muscle force application is the same as the
direction of muscle force action. The intensity of
concentric action is defined as positive muscle power
Pm = Fm × Vm > 0. The amount of concentric action is
defined as the time integral of power Pm or positive
muscle work, Wm > 0. (c) Isometric action takes place
when the magnitude of developed muscle force is equal
to an external force and the point of muscle force
application does not move, Vm = 0. The intensity and
amount of muscle action is zero: Pm = 0 and Wm = 0.
57
Muscle lengths and the rate of their change are
obtained from recorded joint angles and a quantitative description of musculoskeletal geometry
(Morecki et al. 1971; Hatze 1981; Zatsiorsky et al.
1981; Delp et al. 1990; Pierrynowski 1995). The values
of estimated muscle forces and work depend on
model assumptions which are difficult to validate.
A more reliable although indirect method for
muscle power estimation involves determining
power of the resultant joint moment, which reflects
the net effect resulting from action of all muscles
and passive tissue around the joint: Pj = Mj × ωj. In
this product, ωj and Mj are the components of joint
angular velocity and the resultant joint moment
about the joint axis perpendicular to the plane of
interest, and Pj is the power produced by the moment,
or joint power. Mj is calculated from recorded kinematics and external forces applied to the body
using inverse dynamics analysis (Elftman 1939;
Aleshinsky & Zatsiorsky 1978; Winter 1990). The
integral of Pj over the time of muscle action yields
joint work. The power and work of the joint moment
are negative when the directions of Mj and ωj are
opposite (eccentric action, Fig. 4.2a). When Mj and ωj
have the same directions, joint power and work are
positive (concentric action, Fig. 4.2b). When Mj ≠ 0
and ωj = 0, joint power and work are zero (isometric
action, Fig. 4.2c).
Other methods of estimating muscle power and
work are more simple and less accurate and include:
• power and work done against external load;
• ‘external work’;
• ‘internal work’; and
• ‘total work’.
The latter three indices of work are calculated as the
change of external, internal and total energy of the
body, respectively (Fenn 1930; Cavagna et al. 1964;
Pierrynowski et al. 1980). It should be mentioned
that all the above indices of mechanical work represent work of different forces and moments which
related to muscle forces indirectly (Aleshinsky 1986;
Zatsiorsky 1986). Therefore, values of different
indices of work done in human movements vary
greatly (Pierrynowski et al. 1980; Williams &
Cavanagh 1983; Prilutsky & Zatsiorsky 1992).
In this chapter, different aspects of eccentric
muscle action are considered. First, selected facts
58
muscle action in sport and exercise
Eccentric action
Concentric action
Mj
Mj
ωj
Wj =Pj ·dt <0
Mj
ωj
Pj =Mj ·ωj <0
(a)
Isometric action
ωj = 0
Pj =Mj ·ωj >0
(b)
Wj =Pj ·dt>0
Pj = Mj ·ωj = 0
(c)
Wj = Pj ·dt= 0
Fig. 4.2 Definitions of eccentric, concentric and isometric actions based on negative and positive work of joint moment.
(a) The intensity of eccentric action is defined as the negative power of joint moment (Pj = Mj × ωj < 0, where Mj is the
resultant joint moment and ωj is the joint angular velocity). Note that Mj and ωj have opposite directions. The time integral
of Pj defines the amount of eccentric action or negative work of joint moment, Wj < 0. (b) The intensity of concentric action
is defined as the positive power of joint moment (Pj = Mj × ωj > 0; Mj and ωj have the same directions). The time integral of
Pj defines the amount of concentric action or positive work of joint moment, Wj > 0. (c) Isometric action takes place when
the magnitude of the joint moment is equal and opposite to an external moment and there is no joint angle change, ωj = 0.
The intensity and amount of muscle action are zero: Pj = 0 and Wj = 0.
relevant to the behaviour of isolated muscles during the stretch are reviewed below. Based on these
facts, the following section demonstrates how eccentric action may affect various aspects of athletic
performance. Comparisons between physiological
responses to negative and positive work are then
presented in the following section. The final section summarizes quantitative estimates of negative
work done by major muscle groups in selected
athletic events.
Mechanics and energetics of the isolated
muscle during stretch
Muscle mechanical behaviour during and
after stretch
While a fully activated muscle or a fibre is being
stretched from one constant length to another with
moderate speeds, the force recorded on its end
exceeds the maximum isometric force at the same
muscle length (Fig. 4.3). At the end of stretch, the
force can be two times larger than the maximum
isometric force at the same length, so-called ‘force
enhancement during stretch’. This force enhancement is velocity dependent—force typically increases
with the magnitude of stretch velocity (Levin &
Wyman 1927; Katz 1939; Edman et al. 1978). When
the stretch is completed and the muscle length is
kept constant at a new level, force starts decreasing,
but is still larger than the force corresponding to
isometric action. This so-called ‘residual force
enhancement after stretch’ lasts as long as the
muscle is active (Katz 1939; Abbott and Aubert
1952; Edman et al. 1978; Sugi & Tsuchiya 1981;
Edman & Tsuchiya 1996). The residual force enhancement after stretch appears when the muscle is
stretched above the optimal length Lo (the length at
which the muscle develops the maximum force)
(Edman et al. 1978; Edman & Tsuchiya 1996).
Mean SL
eccentric action
59
2.05
1.90
µm
a
Mean SL
Fig. 4.3 Force and displacement
records from a frog single muscle
fibre during tetani at two different
sarcomere lengths (SL). (a) Stretch
during activity from 1.9 to 2.05 µm
sarcomere length compared with
ordinary isometric tetanus at 2.05
µm. (b) Comparison of stretch from
2.50 to 2.65 µm sarcomere length with
isometric tetanus at 2.65 µm. The
velocity dependent force enhancement during stretch is denoted by a,
whereas b indicates the residual force
enhancement after stretch; the latter
appears above optimal sarcomere
length Lo. (From Edman & Tsuchiya
1996.)
0.2
N·mm–2
(a)
2.65
2.50
µm
a
b
0.2
N·mm–2
(b)
The force enhancement during stretch is thought
to be associated with the increased strain of attached
cross-bridges during the stretch (Sugi & Tsuchiya
1988; Lombardi & Piazzesi 1990). The attached
cross-bridges (Ford et al. 1981) and the tendinous
structures ( Jewell & Wilkie 1958) constitute the
series elastic component (SEC) of the muscle. The
force–length (or stress–strain) relationship of the
SEC can be determined in quick-release experiments in which a fully activated muscle is suddenly
released and allowed to shorten against different constant loads ( Jewell & Wilkie 1958). The
stress–strain relationship obtained for the SEC is
non-linear and monotonic (Fig. 4.4): its instantaneous slope (or stiffness of the series component) is
relatively low at low muscle forces and increases
with increasing muscle forces. The area under the
stress–strain curve equals elastic strain energy
stored in the SEC during isometric development of a
given force. The elastic energy is released during a
release of the muscle. The amount of stored strain
1s
energy depends on SEC stiffness, the maximum
force the muscle is able to develop at a given length,
and the maximum SEC elongation. The SEC elongation in skeletal muscles at maximal isometric force
is on average 5% of Lo (Close 1972). As previously
mentioned, the muscle stretch can increase developed force by a factor of two. Correspondingly,
strain energy stored in the SEC after stretching maximally activated muscle may also increase up to two
times (Fig. 4.4). This in turn may contribute to the
ability of the muscle to shorten against heavier loads
at a given shortening velocity or to shorten faster at
a given load compared with a muscle being released
from the isometric state (Cavagna & Citterio 1974).
The influence of stretch on muscle performance is
more pronounced at slow shortening velocities than
at fast ones (Fig. 4.5). Release of a fully activated
muscle immediately after the muscle is stretched
increases positive work done by the muscle up to
two times (Cavagna et al. 1968). The work enhancement was reported to increase with the velocity of
60
muscle action in sport and exercise
among sarcomeres in series ( Julian & Morgan
1979; Morgan 1994; Edman & Tsuchiya 1996). The
force–velocity relationship obtained from a muscle
developing the residual force enhancement after
stretch by releasing it against different constant
loads behaves similar to the force–velocity relationship obtained from a muscle demonstrating the
force enhancement during stretch (Fig. 4.5): the
force–velocity curve shifts to the right with apparently no change in maximum shortening velocity
(Edman et al. 1978).
8
7
Stress (kg·cm–2)
6
5
4
3
2
Energetics of the muscle during stretch
1
0
1
2
3
4
5
6
7
8
Strain (% of L0)
Fig. 4.4 Typical stress–strain curves of the series elastic
component of frog gastrocnemius (solid line), of sartorius
(dashed line) (data from Jewell & Wilkie 1958), and of rat
gracilis anticus (dotted line) (data from Bahler 1967).
The open circles refer to data obtained by releasing the
muscle immediately after stretching, the filled circles by
releasing the muscle in isometric contraction. The stress
is expressed in kg · cm–2 of muscle cross-section and
the strain as a percentage of muscle resting length, Lo.
The lengthening of the series elastic component when
the stress rises to its full isometric value of 5.2 kg · cm−2
is about 3% of the Lo. The elastic energy stored in the
series elastic component of frog gastrocnemius (area
under solid line) up to Po and normalized to muscle mass
is on average 55 g · cm · g–1; an additional amount of
63 g · cm · g–1 is stored during stretching the active
muscle. (From Cavagna 1970.)
the stretch, initial muscle length, and temperature,
and to decrease with a pause between the stretch and
shortening (Cavagna et al. 1968, 1994). The reasons
for this enhancement of positive power and work
are not clear as the elastic energy stored in the
strained cross-bridges is fully discharged by a small
muscle release (for further discussion and references, see Edman & Tsuchiya 1996; Edman 1997).
The residual force enhancement after stretch (Fig.
4.3) is observed if the stretch is performed from an
initial muscle length exceeding Lo. The mechanisms underlying the residual force enhancement are
thought to originate from length non-uniformity
Metabolic energy expenditure (energy liberated and
~P hydrolysis) of isolated skeletal muscles is lower
during stretch of active muscle than during shortening or isometric development of force (Fenn 1923,
1924; Abbot et al. 1951; Curtin & Davies 1975). It was
also reported that a substantial portion of muscle
negative work (work done on the muscle) does not
appear in the total muscle heat production (Abbot
et al. 1951; Hill & Howarth 1959). Abbot et al. (1951)
suggested three possibilities to explain the above
facts:
(a) . . . the work is absorbed in driving backwards
chemical processes which have actually occurred
as a normal part of contraction; (b) . . . the work
is absorbed in some other chemical or physical
process at present unknown; and (c) . . . the work
is wholly degraded into heat, but that chemical
processes normally occurring in contraction are
prevented by the stretch.
Evidence for the first and second possibilities was
not found (Rall 1985; Woledge et al. 1985). It is more
likely that the rate of ATP splitting is reduced
during stretching of active muscle and the negative work is not utilized in the chemical reactions
(Homsher & Kean 1978). The rate of ATP splitting
is especially low at low velocities of stretch and
can be four times lower compared with isometric
force development at the stretch velocity of about
0.2 Lo · s–1 (Curtin & Davies 1975). At higher speeds of
stretching, metabolic energy expenditure increases.
Metabolic energy expenditure approaches the cost
of isometric force development at the velocity which
corresponds to negative power, the absolute value
eccentric action
1100
5
1000
3
900
Force (g)
of which equals the maximum positive power that
occurred during shortening of the muscle (Marechal
1964). With increasing stretch velocities further
eccentric action becomes more expensive in terms
of metabolic energy expenditure compared with
isometric action (Marechal 1964), but still cheaper
than concentric action (Fenn 1923, 1924).
A low rate of ATP splitting also occurs during the
residual force enhancement after stretch (Homsher
& Kean 1978; Curtin & Woledge 1979) despite the
enhanced forces being produced.
+
800
7
4
700
600
1
Dissipation of energy
0
0
6
2
3
8
6,7
45
40
+
5
4
35
3
30
2
20
9
1
25
0
1
2
3
50
2
3
Force (g)
45
Fig. 4.5 Force–velocity relationships of frog gastrocnemius (top; Lo = 2.5 cm, 0.1–0.2°C), frog semitendinosus
(middle; mass = 0.038 g, Lo = 2.5 cm, 0.2– 0.6°C), and frog
sartorius (bottom; mass = 0.058 g, Lo = 3.25 cm, 0.2– 0.7°C).
Filled circles and solid line: release from a state of isometric contraction; open circles and dashed line: release
at the end of stretching. When the muscle is released
immediately after stretching its speed of shortening is
greater than when release takes place from a state of
isometric contraction. In addition, after stretching the
muscle is able to lift a weight greater than the isometric
force at the length of release. The force developed by the
parallel elastic elements before release was about 25 g for
gastrocnemius, and 1 g for semitendinosus and sartorius.
(From Cavagna & Citterio 1974.)
2
1
50
Force (g)
A muscle subjected to periodic stretching and shortening by an attached spring demonstrates damping
of imposed oscillations or, in other words, dissipation of energy of oscillations (for terminology, see
Zatsiorsky 1997). The ability of the muscle to dissipate energy increases with an increase in activation
level (Gasser & Hill 1924) and with the magnitude
of length change (Rack & Westbury 1974). For
example, the damping of oscillation is approximately 40 times greater in an active muscle compared
with a passive one (Fig. 4.6).
A muscle’s ability to dissipate mechanical energy
of the body seems to have important implications
for such athletic activities as landing in gymnastics,
where muscles acting eccentrically have to dissipate energy of the body in a short period of time
(see ‘Dissipation of mechanical energy’). The ability
of muscles to dissipate energy is also important
for preventing joint angles from reaching the
61
40
+
1
4
6
35
30
25
5
0
2
4
Velocity (mm · s–1)
6
62
muscle action in sport and exercise
b
a
limits of their range of motion by decelerating body
segments.
The data reviewed in this section demonstrate that
eccentric muscle action may have important implications for improving athletic performance. First,
stretching active muscles may lead to an enhancement of developed force, work and power during
subsequent isometric and concentric actions. Second,
this enhancement does not require additional metabolic energy expenditure and may increase economy and efficiency of subsequent isometric and
concentric actions.
Influence of eccentric action on
athletic performance
As previously mentioned, eccentric muscle action
can potentially affect performance in athletic activities. A number of studies reviewed in this section
support the above expectation.
Maximum moment production and
muscle activation
The difference in maximum joint moment between different types of muscle action is clearly
seen in moment–angular velocity curves (Fig. 4.7a).
These curves are often obtained using isokinetic
dynamometers which measure exerted moments
at a constant joint velocity. The magnitude of joint
moment is highest during eccentric action—the
c
Fig. 4.6 Damping of oscillations in
a spring connected to a muscle:
(a) unexcited; (b) excited;
(c) unexcited again. The damping
becomes enormously greater when
the muscle is excited. Time marks,
1/5 s. (From Gasser & Hill 1924.)
moment increases with velocity at relatively low
velocity values and then it stays at about the same
level or declines slightly with velocity (for reviews,
see Cabri 1991; Prilutsky 1991). The maximum
eccentric moment exceeds the isometric moment by
approximately 30– 40% (Komi 1973; Barnes 1981;
Cabri 1991), which is a smaller difference than seen
in experiments on isolated muscles (Cavagna &
Citterio 1974; Katz 1939). A smaller enhancement
of eccentric moments in vivo may be partially
explained by the inability of subjects to fully activate
their muscles (Westing et al. 1990; Westing et al.
1991). When subjects’ muscles are electrically stimulated, the difference between maximum eccentric
and isometric moments increases and resembles
results of in vivo experiments (Westing et al. 1990).
The magnitude of maximum eccentric moments
is substantially higher than that of concentric
moments (Fig. 4.7a). Since concentric moments
sharply decline with angular velocity and eccentric
moments do not decrease markedly, the difference
in the magnitude between eccentric and concentric moments becomes larger as absolute values
of angular velocity increase.
The hypothesis that eccentric exercises require
fewer active muscle fibres than concentric exercises with the same resistance (Abbot et al. 1952;
Asmussen 1953) is supported by lower values of
the ratio electromyographic activity (EMG)/force
(or the slope of EMG–force relationship) in eccentric
action compared with concentric action (Fig. 4.8a;
eccentric action
39
37
37
35
35
33
33
31
= Mean ±SE
29
29
27
27
25
25
23
23
21
21
9
Biceps brachii
8
8
7
7
6
6
Brachioradialis
5
5
4
4
M
3
2
= Mean±SE
1
7 6 5 4 3 2 1 0 1 2 3 4 5 6 7
us
cle
3
te
ns
ion
2
1
Triceps brachii
7 6 5 4 3 2 1 0 1 2 3 4 5 6 7
Velocity of contraction (cm·s–1)
(a)
10
9
iEMG (arbitrary units)
39
31
Concentric work
Eccentric work
10
iEMG (arbitrary units)
Concentric work
Muscle tension (kg)
Muscle tension (kg)
Eccentric work
63
Velocity of contraction (cm · s–1)
(b)
250
200
150
100
50
0
(a)
Integrated electrical activity (arbitrary units)
Integrated electrical activity (arbitrary units)
Fig. 4.7 (a) Force–velocity relationship for the human elbow flexor muscles. (b) Integrated EMG (iEMG)–velocity
relationship for the human biceps brachii and brachioradialis muscles and their antagonist (triceps brachii). Muscle
velocity was estimated from joint angular velocity and muscle moment arm; muscle force was estimated from the
measured joint moment and muscle moment arm. (From Komi 1973.)
10
20
30
40
50
3
2
1
0
60
Tension (kg)
4
(b)
0.2
0.4
0.6
0.8
1.0
Velocity (rad · s–1)
Fig. 4.8 (a) The relation between integrated electrical activity and tension in the human calf muscles. Shortening at
constant velocity (solid line) and lengthening at the same constant velocity (dashed line). Each point is the mean of the first
10 observations on one subject. Tension represents weight lifted and is approximately 1/10 of the tension calculated in the
tendon. (b) The relation between integrated electrical activity and velocity of shortening (solid line) and lengthening
(dashed line) at the same tension (3.73 kg). Each point is the mean of the first 10 observations on one subject. (From
Bigland & Lippold 1954.)
see also Asmussen 1953; Komi 1973; Bigland-Ritchie
& Woods 1976; Heckathorne & Childress 1981). The
EMG magnitude does not appear to depend on the
rate of joint angle (or muscle length) changes during
eccentric exercise against a constant resistance,
whereas EMG in concentric exercises increases with
velocity (Fig. 4.8b; see also Eloranta & Komi 1980).
These facts are consistent, in general, with the force–
velocity relationship (Fig. 4.7a). The EMG magnitude during maximum eccentric and concentric
64
muscle action in sport and exercise
Table 4.1 The increase in isometric strength after eccentric, concentric and isometric strength training (selected studies).
Subjects
Muscle group(s)
(programme length)
Eccentric
Concentric
Isometric
Authors
16 men
Leg flexors
Arm flexors
(13 weeks, 2 days
a week, 2 h a day)
53.6 kg of load
6.4 kg
51.9 kg
8.8 kg
Seliger et al. (1968)
26 men
Triceps brachii
(30 days, 5 days a
week, 2 series of
5 repetitions a day)
10.0 kg of load
8.7 kg
Mannheimer (1969)
21 men and
women
Wrist flexors
(10 days, 5 max.
actions a day)
34.5%
31 men
Forearm flexors
(7 weeks, 4 times
a week, 6 max.
actions a day)
2.7 kg of load
actions appears to be similar (Fig. 4.7b; Rodgers &
Berger 1974; Komi & Viitasalo 1977; Seliger et al.
1980; Westing et al. 1990; however, see Enoka 1996).
Several authors have reported differences in
motor unit behaviour between eccentric and concentric actions (Nordone et al. 1989; Howell et al.
1995; Enoka 1996): high-threshold motor units seem
to be used more extensively in eccentric actions than
in concentric actions, and the spike rate of the
involved motor units is lower in eccentric actions
compared with concentric. A larger involvement of
high-threshold motor units in eccentric exercise is
supported by the observation that after intensive
eccentric exercise, signs of muscle fibre damage are
seen more often in type II (fast-twitch) muscle fibres
(Friden et al. 1983), which are controlled by highthreshold motor units. An alternative explanation
for a preferential injury of fast-twitch muscle fibres
in eccentric actions is that fast-twitch fibres may
be more susceptible to stretch-induced damage
because of a less-developed endomysium compared
with slow-twitch fibres (Stauber 1989).
Is eccentric action more advantageous for isometric strength training than isometric and concentric actions because higher muscle forces can
be produced during eccentric action? In most cases,
50.2%
2.0 kg
Moore (1971)
Komi and Buskirk
(1972)
eccentric strength training does not lead to higher
isometric strength and is comparable with isometric
and concentric training (Table 4.1). Even when
eccentric training is shown to be more effective
for increasing isometric strength, it often has sideeffects such as muscle injury and soreness (for
reviews, see Armstrong 1984; Prilutsky 1989; Friden
& Lieber 1992; see also Chapter 28). Therefore, it
appears that combining different types of exercise
is a better method for strength training. It should
be noted that strength training may be action type
specific (Kellis & Baltzopoulos 1995)—eccentric training may improve eccentric strength more than
concentric (see e.g. Hortobagyi et al. 1996b). Some
studies, however, demonstrate similar improvements in eccentric, isometric and concentric strength
after eccentric training (Kellis & Baltzopoulos 1995).
Enhancement of positive work and
power production
As demonstrated above (see ‘Mechanics and energetics of the isolated muscle during stretch’), a
preliminary muscle stretch causes a modification
of the force–velocity relationship during shortening (Fig. 4.5) and increases strain energy stored in
eccentric action
65
Table 4.2 Enhancement of athletic performance immediately after eccentric action (selected studies).
Subjects
Movement
Eccentric action
Performance index
Enhancement
Authors
N=6
22–29 years
Leg extension from
a squat position
Countermovement
Mean power
29%
Thys et al. (1972)
N = 19
Vertical jump
Countermovement
Drop jump from:
0.233 m
0.404 m
0.690 m
Jump height
0.02 m
Asmussen and BondePetersen (1974a)
Jump height
Jump height
Jump height
0.03 m
0.042 m
0.023 m
Vertical jump;
Leg muscle
temperature:
37°C
32°C
Drop jump from 0.4 m
Jump height
Elbow flexion
Countermovement
Elbow extensors
Countermovement
Push of pendulum
Countermovement
at speed:
0.91 m · s−1
1.37 m · s−1
1.82 m · s−1
2.27 m · s−1
2.72 m · s−1
N=5
N=3
N = 18
18–25 years
Asmussen and BondePetersen (1974a)
0.017 m
0.0462 m
the SEC (Fig. 4.4). If these changes of muscle
mechanical properties take place in vivo, they may
increase positive work and power production,
which would be very useful in many athletic activities. Comparisons between positive work and
power (or performance indices related to positive
power, i.e. maximum movement velocity, jump
height, etc.) obtained with and without preliminary
muscle stretch often demonstrate enhancement in
performance by the stretch (Table 4.2). The observed
enhancement in muscle performance may also be
caused by additional activation of muscles being
stretched in the stretch–shortening cycle (SSC)
(Dietz et al. 1979; Bosco et al. 1981). The nature of this
additional activation is unclear, since the gain of
stretch reflex may be low during running (Stein et al.
1993) where the enhanced activation occurs (Dietz
et al. 1979).
The relative contribution to power enhancement of the above three mechanisms (change in
force–velocity curve, increased amount of strain
Positive work
per unit of EMG
23%
Cnockaert (1978)
111%
Pendulum speed
Bober et al. (1980)
0.14 m · s−1
0.19 m · s−1
0.21 m · s−1
0.22 m · s−1
0.24 m · s−1
energy in SEC, and stretch reflex) is not known.
Some authors question the use of strain energy to
enhance positive power in human movements (van
Ingen Schenau 1984; van Ingen Schenau et al. 1997)
suggesting that its contribution is negligible and the
enhancement of muscle performance is the result of
a longer time available during the stretch to achieve
maximum muscle activation before the concentric
phase (van Ingen Schenau 1984; Chapman et al.
1985). Other authors argue, based on their estimations of strain energy stored in human muscletendon complexes, that the contribution of SEC
can be substantial (see e.g. Hof 1998). In animal
locomotion, a substantial (in some cases up to
90%) contribution of SEC strain energy to positive
work and power during muscle shortening has
been demonstrated using direct in vivo measurements of tendon forces (Prilutsky et al. 1996a),
muscle fibre length (Griffiths 1991; Gregersen et al.
1998) or both (Biewener et al. 1998; Roberts et al.
1997).
66
muscle action in sport and exercise
The potential contribution of the stretch reflex to
the enhancement of positive power requires metabolic
energy consumption due to activation of additional
motor units. The energy consumption requirement
of the stretch reflex may be used for a separation of
its contribution to enhanced performance from the
contributions of the other two factors which require
less or no additional energy expenditure (see ‘Energetics of the muscle during stretch’ above). For example, the lowest values of the peak positive power
during the stance phase of running long jumps
reported in the literature are 3000 W, 1000 W, and
2500 W for the ankle, knee, and hip joints, respectively (Tupa et al. 1980; Requejo et al. 1998; Stefanyshyn & Nigg 1998). Such high values of positive
power do not seem to be accounted for by an estimated peak rate of metabolic power output (about
400 W · kg –1 of muscle mass; Hochachka 1985;
Wasserman et al. 1986) and estimated mass of ankle,
knee and hip extensors (from Yamaguchi et al. 1990).
Thus, it is likely that there is an enhancement of
positive mechanical power output in running long
jumps that cannot be accounted for without the use
of strain energy in SEC and/or the enhancement of
the contractile mechanism leading to the shift of the
force–velocity relationship.
The peak values of joint positive power in explosive movements performed immediately after the
stretch exceed several times the maximum power
measured or estimated from the force–velocity or
moment–angular velocity curves of the same muscle groups (van Ingen Schenau et al. 1985; Edgerton
et al. 1986; Gregor et al. 1988; Prilutsky et al. 1992),
which is in agreement with the notion of enhancement of positive work and power by the muscle
stretch.
Whatever the relative contribution of the three
previously described factors to the enhancement of
positive power and work in athletic performance
might be, their combined effect appears to be substantial (Table 4.2). The performance enhancement
depends on the rate of muscle stretch (Asmussen &
Bonde-Petersen 1974a; Bober et al. 1980; Bosco et al.
1981), the time of transition from the stretch to shortening (Thys et al. 1972; Bosco et al. 1981), the percentage of slow-twitch fibres in the muscle (Viitasalo &
Bosco 1982), muscle mechanical properties (Aruin
& Prilutsky 1985), muscle temperature (Asmussen
et al. 1976), gender (Komi & Bosco 1978; Bosco &
Komi 1980), and age (Bosco & Komi 1980).
Economy and efficiency of positive work
Economy of positive work can be defined as positive mechanical work done per unit of metabolic
energy spent. Since there are many ways to
determine positive mechanical work done (see
‘Definitions of eccentric muscle action and negative work and power’ above) and metabolic
energy spent (Whipp & Wasserman 1969; van Ingen
Schenau et al. 1997) during human movements,
there are many indices of economy of positive
work. Efficiency of positive work can be defined
(for details, see Prilutsky 1997; Woledge 1997) as:
ep = Wp/(∆E + Wn), where ep is the efficiency of
positive work, Wp and Wn are, respectively, the
total positive and negative work done by muscles,
and ∆E is chemical energy released from the
muscles (which can be assessed by measuring the
total metabolic energy spent). The term ep can have
different values depending on how Wp , Wn, and ∆E
are measured; ep cannot, however, exceed 1.
Given the facts reviewed in sections above it can
be expected that economy and efficiency of positive
work performed immediately after negative work
(i.e. after muscle stretch) would exceed those of
positive work done without a preliminary stretch.
First, SEC is able to store more strain energy when
the muscle is stretched compared with an isometric
force development (Fig. 4.4). This additional energy
can potentially be used in the subsequent shortening (see, however, Edman 1997, who questions such
a possibility). Second, the shift of the force–velocity
curve to the right (Fig. 4.5) does not require additional energy expenditure. Furthermore, energy
expenditure required to resist the stretch (to do
negative work) is relatively low (see ‘Energetics
of the muscle during stretch’ above; and ‘Oxygen
consumption during eccentric and concentric exercise’ below).
Experimental studies demonstrate that indices of
positive work economy in movements where positive work is done immediately after a substantial
amount of preliminary muscle stretch—in level
eccentric action
running (Lloyd & Zacks 1972; Asmussen & BondePetersen 1974b; Cavagna & Kaneko 1977), in countermovement jumping (Asmussen & Bonde-Petersen
1974b; Thys et al. 1975; Aruin et al. 1977; Bosco et al.
1982; Kaneko et al. 1984; Voight et al. 1995), and in
squatting (Aruin et al. 1979; Thys et al. 1972)—have
higher values compared with the same indices
obtained during walking and running uphill or
cycling where muscles supposedly do little or no
negative work (Margaria 1938; Whipp & Wasserman 1969). According to estimates of some authors,
the contribution of the preliminary stretch to the
increase of economy of positive work is 35–53%
in running (Cavagna et al. 1964; Asmussen &
Bonde-Petersen 1974b), 27–34% in squatting
(Asmussen & Bonde-Petersen 1974b; Thys et al.
1972; Aruin et al. 1979), 30–60% in jumping (Bosco
et al. 1982; Thys et al. 1975; Voight et al. 1995), and
23% in level walking (Asmussen & Bonde-Petersen
1974b).
Simultaneous in vivo measurements of forces and
fibre length changes of selected ankle extensor muscles during running in turkey (Roberts et al. 1997)
and tammar wallabies (Biewener et al. 1998) show
that most of the positive work done by the studied
muscle-tendon complexes resulted from the release
of tendon and/or aponeurosis strain energy. As
mentioned previously, the contribution of SEC
strain energy to positive work in human movements is still under debate.
Dissipation of mechanical energy
In many athletic events which involve landing, the
body experiences very high impact forces: the
vertical ground reaction force can reach values that
exceed body weight by 14 times (Tupa et al. 1980;
DeVita & Skelly 1992; McNitt-Gray 1993; Simpson &
Kanter 1997; Requejo et al. 1998), which may result
in injuries (Dufek & Bates 1991; Nigg 1985). Two
types of injury may occur due to extreme loads:
injuries of passive anatomical tissue (ligaments, cartilage, intervertebral discs, etc.) and injuries of muscles. The mechanisms underlying both injury types
are not yet precisely understood. If it is proven that
the amount of mechanical energy absorbed by the
passive tissues during landing impact is a major
67
contributor to their damage, then the ability of
active muscles to dissipate mechanical energy (see
‘Dissipation of energy’ above) may be very useful in
protecting passive anatomical structures.
The amount of mechanical energy passively dissipated can be estimated during barefoot landing
on a stiff force plate after a drop jump (Zatsiorsky
& Prilutsky 1987). To make this estimation, the percentage of energy dissipated by muscles is obtained
as
Total negative work of joint
moments during landing
× 100%
ISL =
Reduction in total energy of
the body during landing
(4.1)
where ISL is the index of softness of landing (see
below). In this approach, it is assumed that the total
negative work done by joint moments during the
landing is equal to the total negative work done by
muscles, and that the nominator and denominator are equal during very soft landings. The latter
assumption was verified. In maximally soft landings, the total negative work of joint moments and
the reduction in total energy of the body were equal
within the accuracy of measurements (Zatsiorsky &
Prilutsky 1987; Prilutsky 1990). Note that in walking, running and other activities where power in
different joints and changes in kinetic and potential
energy of different segments do not always have the
same sign, the total work of joint moments and the
change in total energy of the body are not equal
(Aleshinsky 1986; Zatsiorsky 1986). The index ISL
represents the percentage of total energy of the
body just before landing, which is dissipated by the
muscles. The rest of the body’s energy is dissipated
by passive structures. In the maximum stiff landings that the subject could perform, up to 30% of
the energy was dissipated passively (Zatsiorsky &
Prilutsky 1987). If landing is performed on the
heels by keeping the legs straight, no joint work
will be done and all the energy of the body will be
dissipated in the passive anatomical structures.
Needless to say it would be very harmful for the
body. It appears that athletes are able to regulate
muscle behaviour during landing in order to maximize either ‘spring’ or damping properties of the
muscles (Dyhre-Poulsen et al. 1991).
68
muscle action in sport and exercise
The ability of damping high impact accelerations
in downhill skiing discriminates well between good
and inexperienced skiers (Nigg & Neukomm 1973).
Fatigue compromises the ability to attenuate and
dissipate impact shock waves during running
(Verbitsky et al. 1998; Voloshin et al. 1998), which
suggests the involvement of active muscles in
damping impact loads. It should be noted here that
the enhancement of positive power and economy
of positive work immediately after the stretch (see
‘Economy and efficiency of positive work’ above)
and dissipation of energy of the body to protect
passive anatomical structures appear to be conflicting demands, and maximizing one property
would lead to compromising the other (DyhrePoulsen et al. 1991).
In several joints of the swing leg and the upper
extremities, negative power is developed prior to
their range of motion limit (Morrison 1970; Winter
& Robertson 1978; Tupa et al. 1980; Prilutsky 1990,
1991). For example, the knee flexor muscles dissipate energy of the shank and prevent an excessive
knee extension in the end of the swing phase during
walking and running (see ‘Negative work in athletic
events’ below). Another example of keeping joints
within their range of motion by eccentric muscle
action is the ‘articulation’ between the pelvis and
the trunk whose relative rotation in the horizontal
plane is controlled by muscles developing negative
power (Prilutsky 1990). Thus, the muscle’s ability
for energy dissipation and damping of high-impact
forces appears to play an important role not only in
attenuating and dissipating impact shock waves,
but also in protecting joints from exceeding their
range of motion.
Electromechanical delay
The electromechanical delay (EMD) is the interval
between the onset of muscle electromyographic
activity and developed force or joint moment.
According to the literature, EMD ranges from about
30 ms to 100 ms and higher (Cavanagh & Komi
1979; Norman & Komi 1979; Vos et al. 1991) and
therefore constitutes a rather large part of the total
reaction time, the time interval from the presentation of an unexpected stimulus to the initiation of
the response (see e.g. Schmidt 1988). The type of
muscle action affects the duration of EMD. The
shortest EMD typically occurs during eccentric
action. For example, EMD determined for the
biceps brachii during eccentric action is 38 ms (at
the slow joint angular velocity) and 28 ms (at the
faster velocity), whereas EMD during concentric
action is 41 ms and is independent of joint velocity
(Norman & Komi 1979). It is thought that a major
portion of EMD is associated with the stretch of the
SEC to a point where muscle force can be detected
(Cavanagh & Komi 1979; Norman & Komi 1979;
Grabiner 1986). Therefore, it seems that conditions
for a rapid force development are more advantageous during eccentric action (Cavanagh & Komi 1979).
Fatigue and perceived exertion during
eccentric action
Two major types of exercise-induced fatigue can be
distinguished (Green 1997):
1 Metabolic fatigue, which is related to a failure to
maintain desired ATP production rates and tolerate
high accumulation of by-products of metabolic
reactions.
2 Non-metabolic fatigue, caused by high internal
muscle stress, which is believed to be associated
with a disruption of internal muscle structures.
Eccentric muscle action is much less metabolically
demanding than concentric and isometric actions
(see ‘Energetics of the muscle during stretch’
above; and ‘Oxygen consumption during eccentric
and concentric exercise’ below), and force per
number of active muscle fibres is likely to be substantially higher during eccentric action compared
with that of concentric and isometric actions (see
‘Maximum moment production and muscle activation’ above). Therefore, differences in fatigue
between eccentric and other types of muscle action
can be expected.
Moderate eccentric muscle action appears to
cause substantially lower fatigue (smaller declines
in developed force and power; Crenshaw et al. 1995;
Hortobagyi et al. 1996a) and perceived exertion
(Henriksson et al. 1972; Pandolf et al. 1978) compared with concentric action of the same intensity.
Note that fewer muscle fibres are activated during
eccentric exercise compared with concentric and
isometric exercise against the same load.
eccentric action
During eccentric exercise of high intensity (corresponding to 90% of maximum oxygen uptake
(Vo2-max) in the corresponding concentric exercise),
the subjects are reportedly incapable of continuing
exercise for longer than 30 min (Knuttgen 1986). At
the point of exhaustion, none of the signs of exhaustion typical for concentric exercise (high values of
Vo2 uptake, heart rate, muscle and blood lactate,
etc.) are present (Knuttgen 1986). After 6 weeks of
eccentric training with the same intensity, the subjects become able to continue exercise for several
hours (Bonde-Petersen et al. 1973; Knuttgen et al.
1982). It has been thought that inability of untrained
subjects to continue eccentric exercise is caused by
damage of muscle fibres and inappropriate motor
unit recruitment (Knuttgen 1986).
When eccentric and concentric actions are compared at the same oxygen consumption level or
when eccentric and concentric exercises are performed with maximum effort, muscles fatigue faster
in eccentric exercise (Komi & Rusko 1974; Komi &
Viitasalo 1977; Jones et al. 1989). Hence, perceived
exertion in eccentric exercise is higher than in the
corresponding concentric exercise (Henriksson et al.
1972; Pandolf et al. 1978). Note that muscles develop
higher forces in maximum eccentric than in maximum concentric exercise (Fig. 4.7).
Long-lasting SSC exercises (consisting of both
eccentric and concentric actions) reduce the enhancement of positive work and power (Gollhofer et al.
1987; Avela & Komi 1998).
Physiological cost of eccentric action
In this chapter, we consider differences in physiological responses of the body to negative and
positive work (eccentric and concentric actions).
Several methods of setting equivalent magnitudes
of negative and positive work have been used to
study physiological differences between eccentric
and concentric exercises. Most of the methods
ensure that the subjects produce the same forces or
moments at the same absolute values of the rate of
muscle length or joint angle change in eccentric and
concentric exercise. Three major groups of methods
have been used most.
1 Lifting and lowering load (Chauveau 1896b).
2 Going up and down stairs (Chauveau 1896a)
69
Fig. 4.9 Schematic drawing of a bicycle on the inclined
treadmill. Arrangement for uphill and downhill riding.
(From Asmussen 1953.)
or walking and running uphill and downhill
(Margaria 1938).
3 Cycling forwards and cycling backwards resisting the pedal rotation (Abbot et al. 1952; Asmussen
1953) (Fig. 4.9).
Mechanical work performed in the first group of
methods is estimated as the product of load weight
and the load displacement (upward direction is
positive). During walking and running on incline
surfaces, work done to raise or lower the centre
of mass of the body is determined as Wp/n = ∆Epot =
w · s · sin φ, where Wp/n is positive or negative
work, ∆Epot is the change of potential energy of
the body, w is body weight (body mass in kg times
9.81 m · s–2), s is the distance travelled on the incline
surface (positive for uphill and negative for downhill), and φ is the slope of the surface with respect to
the horizon (in radians). It should be mentioned that
subjects’ movements during uphill and downhill
walking are not identical. Comparisons between
walking uphill forwards and downhill backwards
would be better in that sense (Chauveau 1896a;
Hill 1965, p. 151). However, the physiological cost
of unnatural backward locomotion would likely
be altered, which would complicate comparisons
of responses to uphill and downhill locomotion
(Margaria 1938). In bike ergometer riding, work
done is determined from a given resistance. Values
70
muscle action in sport and exercise
of positive and negative work done while moving
on inclined surfaces and during cycling, determined
as described above, are smaller than values of positive and negative work of joint moments (Williams
& Cavanagh 1983; Prilutsky & Zatsiorsky 1992).
However, different estimates of muscle work in
walking, running and jumping (external work,
total work, and total work of joint moments) are
correlated (Prilutsky 1990; Prilutsky & Zatsiorsky
1992).
Oxygen consumption during eccentric and
concentric exercise
One of the most important variables characterizing
physiological responses to exercise is oxygen uptake, which reflects metabolic energy expenditure.
The rate of oxygen uptake (Bo2) during a
‘steady state’ exercise (when Bo2 uptake corresponds to the demands) increases with negative
power. The relationship between Bo2 and Cn is
linear in the range of 0 to –260 W during cycling
(Abbot et al. 1952; Asmussen 1953; Hesser et al.
1977), descending stairs (Kamon 1970; Pandolf et al.
1978), and load lowering by the arm (Monod &
Scherrer 1973). During walking and running downhill, the relationship between Bo2 and Cn is not
linear (Davies et al. 1974). In the range of negative
power of 0 to –260 W, the rate of total oxygen uptake was reported to change from 0.3 l · min–1 to
1.6 l · min–1.
Oxygen uptake during negative work production
is lower than that during positive work (Table 4.3).
The ratio of oxygen uptake during eccentric and
concentric exercise with the same absolute values
of work done (+Bo2/–Bo2) always exceeds 1 and
depends on exercise (walking, running, cycling,
etc.), velocity of movement, and methods of determining Bo2 (gross oxygen uptake, gross oxygen
uptake minus oxygen uptake at rest, etc.). For example, the ratio +Bo2/–Bo2 during cycling exercise
increases with cadence from about 2 at 15 r.p.m. to
5.2–10 at 100 r.p.m. (Abbot et al. 1952; BiglandRitchie & Woods 1976). Asmussen (1953) reported
a ratio of 125 at a cadence of 102 r.p.m. Eccentric
training decreases the metabolic cost of performing
negative work and increases the ratio +Bo2/–Bo2 up
to two times (Davies & Barnes 1972a). Cessation
of training for 3 – 4 months causes –Bo2 to return to
the pretraining values (Klausen & Knuttgen 1971;
Knuttgen et al. 1971).
The fact that the ratio +Bo2/–Bo2 exceeds 1 can be
explained by the hypothesis that eccentric actions
require fewer active fibres compared with the concentric actions against the same load (see ‘Maximum moment production and muscle activation’
above). The same hypothesis can be used to explain
the increase of the oxygen uptake ratio with the
speed of movement: the difference in the maximum
developed force between eccentric and concentric
actions increases with the speed of muscle length
change (Fig. 4.7a). In addition, a lower oxygen uptake of eccentric actions per unit of muscle activation can also contribute to the high +Bo2/–Bo2 ratio.
According to Bigland-Ritchie and Woods (1976),
Bo2 per unit of integrated EMG of working muscles
is about three times lower in eccentric actions compared with concentric.
Pulmonary ventilation in eccentric exercise
The pulmonary ventilation BE per unit of Bo2 is
slightly higher while performing negative work than
during positive work (Asmussen 1967; D’Angelo
& Torelli 1971; Davies & Barnes 1972b). This fact is
probably not related to a change in the sensitivity of
chemoreceptors for CO2 during eccentric actions,
which is supported by similar slopes of the relationship BE vs. alveolar partial pressure of CO2 (PAco2)
during negative and positive work (Davies &
Barnes 1972b; Miyamura et al. 1976) and by lower
values of PAco2 during negative compared with
positive work (Davies & Barnes 1972b). It was
suggested that the increased ratio BE/Bo2 during
negative work is a reflection of a higher neurogenic
respiratory drive during eccentric exercise due to
larger muscle forces (up to 5 –7 times) in eccentric
exercise at the same Bo2 level as in concentric exercise (Asmussen 1967; D’Angelo & Torelli 1971).
Other indices of ventilatory performance, BE/
Bco2, BE/BT (BT, the mean expired tidal volume),
and PVco2/Bco2, are approximately the same during eccentric and concentric exercise (Davies &
Barnes 1972b; Hesser et al. 1977).
eccentric action
71
Table 4.3 The ratio of oxygen uptake during performing positive and negative work (+Bo2/−Bo2) in equivalent
concentric and eccentric exercises (selected studies).
Subjects
Exercise
2 men
Cycling, 41–213 W:
25.0 r.p.m.
35.4 r.p.m.
52.0 r.p.m.
2.4
3.7
5.2
Cycling, 25 –262 W:
45 r.p.m.
68 r.p.m.
85 r.p.m.
92 r.p.m.
102 r.p.m.
5.9
7.4
13.7
44.5
125
1 man
2 men
Stair walking,
cadence 12 min−1
Stair height (m):
0.2
0.3
0.4
(+Bo2/−Bo2)
Authors
Abbott et al. (1952)
Asmussen (1953)
Nagle et al. (1965)
2.9
3.0
3.2
8 women,
42–51 years
Stair walking,
slope 27– 40°
1.5–1.8
Richardson (1966)
4 men and
women
Walking uphill
and downhill
3.7
Kamon (1970)
7 men
Cycling, 48–230 W
2.7
Bonde-Petersen et al. (1972)
3 men
Load raising and
lowering by the
arm, 3.0 –9.8 W
3.0
Monod & Scherrer (1973)
4 men and
women
Cycling, 25 –164 W:
30 r.p.m.
50 r.p.m.
80 r.p.m.
100 r.p.m.
15 men
Stair walking, slope
± 30°, vertical speed
0.067– 0.25 m · s−1
Heart responses to eccentric exercise
There are varying opinions about differences in
the heart rate, cardiac output and stroke volume
between eccentric and concentric exercises at the
same Bo2 level (Thomson 1971; Monod & Scherrer
1973). However, many authors agree that the conditions for increasing the stroke volume are more
favourable during eccentric exercise than during
concentric exercise with the same oxygen uptake.
4.9
6.6
8.3
10.2
5.3
Bigland-Ritchie and
Woods (1976)
Pandolf et al. (1978)
In eccentric exercise, the venous blood return is
larger due to higher muscle forces developed. High
muscle forces during eccentric exercise also cause
elevated arterial mean pressure and peripheral
resistance (Thomson 1971).
Temperature regulation
Heat stress during eccentric exercise is expected
to be higher than during concentric exercise with
72
muscle action in sport and exercise
the same oxygen uptake because during eccentric
exercise, work done on muscles (i.e. negative work)
is dissipated in muscles. To prevent an excessive
rise of core temperature during eccentric exercise,
the system of temperature regulation provides a
higher temperature gradient between muscles and
skin, a higher blood flow through the skin, and a
more intensive sweat secretion compared with concentric exercise with the same Bo2 (Nielsen 1969;
Smiles & Robinson 1971; Davies & Barnes 1972b;
Nielsen et al. 1972). For example, at an air temperature of 20°C, the difference in the sweat secretion
between negative and positive work with the same
oxygen uptake is about 0.25 l · h–1 (Nielsen et al.
1972). In similar conditions, the muscle temperature is about 2°C higher in eccentric than in concentric exercise (Nielsen 1969; Nadel et al. 1972). The
latter observation may affect muscle metabolism
and the oxygen dissociation curve of the blood in
muscles.
Negative work in athletic events
In most of the athletic events, there are phases of
movement where the total mechanical energy of
the body or some of its segments decreases. This
decrease of energy can be caused by external forces
(e.g. air or water resistance) and/or by forces developed by muscles and passive anatomical structures
such as ligaments, cartilage, etc. In some activities,
for example swimming, rowing, road cycling with
high speeds, and ergometer cycling against high
resistance, the mechanical energy of the athlete is
dissipated mostly by external forces, and muscles
are likely to do little or no negative work. In activities performed at relatively low speeds on stiff
surfaces without slippage, the contribution of external forces to work done on the body is small (for
review, see Zatsiorsky et al. 1982; van Ingen Schenau
& Cavanagh 1990), and muscles do a substantial
amount of negative work. In this section we will
analyse events in which muscles do an appreciable
amount of negative work: running, normal and race
walking, running long and high jumps, and landing. It is assumed here that the work done by the
joint moments is the most accurate estimate of
muscle work.
Normal and race walking
During walking at constant speeds, absolute values
of negative and positive work done in the major
joints of the body are approximately the same
(Prilutsky & Zatsiorsky 1992). In the cycle of normal
walking at speeds of 1.6 –2.4 m · s–1, estimates of
the total negative work summed across the three
orthogonal planes and major joints (three joints for
each lower and upper extremity, and also trunk
and head-trunk articulations) range between –125
and –190 J (Aleshinsky 1978; Zatsiorsky et al. 1982;
Prilutsky & Zatsiorsky 1992). Most of the negative
work is done (or energy is absorbed) by the joints of
the lower extremities (76 –88% of the total negative work: Aleshinsky 1978; Prilutsky & Zatsiorsky
1992). Approximately 77– 87% of the negative work
of the lower extremities is done in the sagittal plane
(Aleshinsky 1978; Zatsiorsky et al. 1982; Prilutsky &
Zatsiorsky 1992; Eng & Winter 1995).
There are several phases of the walking cycle
where moments of the lower extremity absorb
mechanical energy (Fig. 4.10; Eng & Winter 1995).
After the touchdown during approximately the first
10% of the cycle, the ankle flexors sometimes act
eccentrically to decelerate the forward rotation of
the foot (this phase is absent in Fig. 4.10). When the
distal portion of the foot touches the ground, the
ankle extensors start acting eccentrically and absorb
energy during 10 – 40% of the walking cycle (phase
A1-S, Fig. 4.10), just before the phase of energy
generation by the ankle extensors at the end of the
stance phase (40 – 60%, phase A2-S in Fig. 4.10). The
muscles crossing the ankle do –5 to –9 J of negative
work, which is 16 –19% (or 32– 48 J) of the positive
work done at the ankle (Winter 1983a; Prilutsky &
Zatsiorsky 1992; Eng & Winter 1995). The knee
moment produced by the knee extensors mostly
absorbs energy during the stance phase (Fig. 4.10).
In the second half of the swing phase, knee flexors
decelerate forward rotation of the shank by developing negative power, which can exceed 100 W
(phase K4-S in Fig. 4.10) (Morrison 1970; Prilutsky &
Zatsiorsky 1992; Eng & Winter 1995). Negative work
done in the knee during walking with different
speeds has been reported to be between –17 and –61 J,
whereas positive work values range between 1.4 and
eccentric action
Ankle joint powers (W ·kg–1)
6.0
A2–S
Sagittal
0.0
A1–S
–1.5
0
20
40
60
80
100
Per cent of stride
Knee joint powers (W · kg–1)
1.2
K0–S
K2–S
Sagittal
0.0
K1–S
K4–S
K3–S
–2.5
0
20
40
60
80
100
Per cent of stride
2.5
Hip joint powers (W · kg–1)
H1–S
H3–S
Sagittal
0.0
H2–S
–2.0
0
20
40
60
80
100
Per cent of stride
Fig. 4.10 Joint powers normalized to body mass in the
sagittal plane during normal walking. The stance phase
starts at 0% and ends at about 60% of the stride time.
(Adapted from Eng & Winter (1995), pp. 754 –56, with
permission from Elsevier Science.)
73
14 J (Winter 1983a; Prilutsky & Zatsiorsky 1992; Eng
& Winter 1995). The hip flexor muscles decelerate
the thigh extension during approximately the last
third of the stance phase (Fig. 4.10, phase H2-S) and
do –11 to – 60 J of negative work in the sagittal plane
(Prilutsky & Zatsiorsky 1992; Eng & Winter 1995).
The conditions for the enhancement of the positive muscle power and work in walking do not
appear to be favourable. The phases of positive
power generation in the ankle and hip during the
stance phase (phases A2-S and H1-S, respectively,
Fig. 4.10) are not preceded by a substantial amount
of negative work done. Small enhancement of positive power and work may theoretically occur at the
ankle during the end of the stance phase and at the
hip at the beginning of the swing phase. The knee
moment generates little positive work. As mentioned
above, the economy of positive work in walking is
only slightly higher than that of walking uphill or
cycling (Asmussen & Bonde-Petersen 1974b) where
presumably little or no negative work is done.
If power produced by each muscle was known,
estimates of total negative and positive work done
by all muscles could differ from the above values of
joint moment work, even if one assumes no coactivation between antagonistic muscles. The presence
of two-joint muscles may decrease the negative and
positive work required at the joints (Elftman 1940;
Morrison 1970; Wells 1988; Prilutsky & Zatsiorsky
1992; Prilutsky et al. 1996b) due to opposite angle
changes in the adjacent joints and therefore smaller
total length changes of two-joint muscles.
In race walking, the amount of negative and positive work done is larger compared with work in
normal walking at an average speed. At the race
walking speed of 3.2 m · s–1, the total negative work
done in 14 joints and three orthogonal planes estimated from Aleshinsky (1978) is 352.1 J. From this
amount, 286 J or 81% is done in joints of the lower
extremities. Most of the negative work of the lower
extremity is done in the sagittal plane (87– 89%;
Aleshinsky 1978; Zatsiorsky et al. 1982). The patterns
of power in joints of the lower extremity in the sagittal plane during race walking are somewhat similar
to the corresponding patterns in normal walking
(Tupa et al. 1980; Zatsiorsky et al. 1980), despite the
fact that the kinetic and potential energy of the
74
muscle action in sport and exercise
body’s centre of mass change in phase in race walking and out of phase in normal walking (Zatsiorsky
et al. 1980, 1982; Cavagna & Franzetti 1981). The
magnitude of linear segment and angular joint displacements and EMG are greatly exaggerated during
race walking as opposed to normal walking (Murray
et al. 1983; Zatsiorsky et al. 1980). Correspondingly,
the work of joint moments during race walking is
larger. The biggest difference in work between race
and normal walking occurs in the elbow and shoulder
joints in the sagittal plane (5- to 15-fold), in the
‘pelvis-trunk’ articulation in the sagittal and frontal
planes (threefold), and the knee and hip joints
in the sagittal and frontal planes (up to fourfold)
(Aleshinsky 1978; Zatsiorsky et al. 1982).
It has been suggested, based on in-phase changes
in kinetic and potential energy of the centre of body
mass in race walking and in running, that the
efficiency of race walking should be higher than that
of normal walking due to apparently better conditions for the use of elastic energy in race walking
(Cavagna & Franzetti 1981). The similarity of power
patterns in the leg joints between normal and race
walking does not support this suggestion.
Pain in the anterior aspect of the lower leg appears
to be a common problem among race walkers (Sanzen
et al. 1986). It is feasible that this syndrome is partly
caused by high values of negative power and work
produced by the ankle flexors. At the beginning of
the stance phase, the ankle is extending (and the
ankle flexor muscles are being stretched) after the heel
strike and the ankle flexors are active (Zatsiorsky
et al. 1980; Murray et al. 1983; Sanzen et al. 1986). The
increase in velocity of walking from 1.4 m · s–1 to
3.3 m · s–1 results in the increase of anterior tibial compartment pressure (and presumably muscle force)
by approximately five times (Sanzen et al. 1986).
Stair descent
During stair descent, work done by moments at the
knee and ankle is mostly negative, whereas very little negative or positive work is done in the hip joint
(Fig. 4.11a; McFadyen & Winter 1988). The ankle
Muscle powers in ascent (N = 8)
H1
0
–200
200
K4
0
K2
K5
–200
K1
–400
K3
–600
200
A3
0
A2
–200
–400
–600
A1
RTO
0
(a)
H3
RFC LTO
20
40
LFC
60
Per cent of stride
80
Hip power (W)
Gen.
H2
300
200
100
0
–100
Knee power (W)
Gen.
200
300
200
100
0
–100
Ankle power (W)
Gen.
Ankle power (W)
Absorption
Knee power (W)
Absorption
Hip power (W)
Gen.
Muscle powers in descent (N =8)
400
300
200
100
0
–100
100
H1
H3
K1
K2
K3
K4
A3
A2
A1
RFC LTO
0
(b)
H4
20
LFC
40
RTO
60
LFC
80
100
Per cent of stride
Fig. 4.11 Ensemble average and one standard deviation band of muscle powers at each joint in the sagittal plane during
stair descent (a) and ascent (b). RTO, Right toe-off; RFC, right foot contact; LTO, left toe-off; LFC, left foot contact.
(Reprinted from McFadyen & Winter (1988), pp. 738 – 39, with permission from Elsevier Science.)
eccentric action
Prilutsky & Zatsiorsky 1992). Joint moments of the
lower extremity do most of the negative work (80%;
Prilutsky & Zatsiorsky 1992). From this amount,
lower-extremity moments in the sagittal plane do
82% of negative work (Prilutsky & Zatsiorsky
1992).
Joint moments at the ankle and knee in the sagittal
plane (ankle and knee extensors) absorb energy during approximately the first half of the stance phase
and generate energy in the second half of the stance
phase (Fig. 4.12; Tupa et al. 1980; Winter 1983b; Ae
et al. 1987; Buczek & Cavanagh 1990; Prilutsky &
500
Hip
250
0
–250
–500
–750
–1000
1400
Knee
700
Power (W)
extensors absorb energy during approximately the
first third of the stance (A1; weight acceptance
phase). During this phase, the knee extensors are
also active and generate negative power (phase
K1, Fig. 4.11a). The ‘controlled lowering phase’
(McFadyen & Winter 1988) lasts from about midstance to the beginning of swing and is performed
by the knee extensors, which absorb the energy
of the body (Fig. 4.11a, phase K3; Morrison 1970;
McFadyen & Winter 1988). Thus, during stair
descent, most of the work done by joint moments is
negative, and the ankle and knee extensors absorb
most of the energy. The opposite is true for stair
ascent—the knee and ankle extensors do most of the
positive work, whereas all three lower-extremity
joints absorb little energy (Fig. 4.11b; McFadyen &
Winter 1988). These data support the assumption
implied in the studies of physiological responses to
positive and negative work (see above) that during
stair descent and ascent muscles do negative and
positive work, respectively. It should be noted that
the work estimated from the change in total energy
of the centre of mass of the entire body is very close
to the work of joint moments during stair walking
(assuming the arms do not move much) because, as
evident from Fig. 4.11, the power in different joints
essentially does not have opposite signs. In movements where the signs of power in different joints
are the same, the work of joint moments is similar to
the change in total energy of the centre of mass
(Aleshinsky 1986; Zatsiorsky 1986).
0
–700
–1400
1200
Level, downhill and backward running
In running at constant relatively low speeds, as in
walking, absolute values of the total negative and
positive work of joint moments summed across
major joints of the body and across three orthogonal
planes are approximately the same (Prilutsky &
Zatsiorsky 1992). During sprint running with a constant speed, the amount of the total positive work
should be slightly higher than the absolute value of
the total negative work due to work done against
the aerodynamic drag force (Zatsiorsky et al.
1982). The total negative work of joint moments
per cycle ranges from –241 J to –883 J for speeds
of 3.3 – 6.0 m · s–1 (Aleshinsky 1978; Prilutsky 1990;
75
Ankle
600
0
–600
–1200
0
20
40
60
80
100
Relative time (%)
Fig. 4.12 Joint power curves in the sagittal plane from a
representative subject during the stance phase of running.
Solid line and dotted lines are mean ± 1 standard
deviation in normal running. Dashed line is mean in
running with a knee brace. Running speed 3.83 m · s–1.
(Reprinted from DeVita et al. (1996), p. 586, with
permission from Elsevier Science.)
76
muscle action in sport and exercise
Zatsiorsky 1992; DeVita et al. 1996). According to
the literature during running at different constant
speeds, values of negative and positive work done
at the ankle range from –13 to –79 J and from 59
to 106 J, respectively; corresponding values for the
knee joint are –30 to –210 J and 25 to 51 J (Buczek
& Cavanagh 1990; Winter 1983b; Prilutsky &
Zatsiorsky 1992; Stefanyshyn & Nigg 1997). The hip
joint power in the stance is more variable and its
pattern appears to depend on speed. In the swing
phase, the knee joint moments mostly absorb
energy—the knee extensors decelerate knee flexion
in the first half of the swing, and the knee flexors
decelerate knee extension in the second half of the
swing. The hip flexors typically absorb energy at
the end of the stance phase to decelerate hip extension; during the first part of the swing, the hip
flexors accelerate hip flexion; and in the second
half of the swing, the hip extensors decelerate hip
flexion and accelerate hip extension. Metatarsophalangeal joint moments (plantarflexors) mostly
absorb energy during the stance phase of running
at 4.0 and 7.1 m · s–1; corresponding values of negative work are –20.9 J and –47.8 J (Stefanyshyn &
Nigg 1997).
The fact that the energy-generation phase in
the stance of running follows immediately after
the energy absorption phase (Fig. 4.12) and that
absolute values of the negative and positive work
done by the ankle and knee extensors during the
stance are similar support the notion that conditions for the enhancement of positive work and
work economy are more favourable in running than
in walking (Cavagna et al. 1964; Farley & Ferris
1998).
In the stance phase of backward running, the knee
extensors are primary generators of energy and do
very little negative work (DeVita & Stribling 1991).
The ankle extensors still absorb energy in the first
half of the stance phase and generate energy in the
second half, but the amount of negative and positive
work done by them is approximately 50% less
than in forward running (DeVita & Stribling 1991).
Thus, it can be speculated that the efficiency of
positive work in backward running is lower than
in forward running, because the major energy
generators in backward running, the knee extensors, do not absorb energy prior to the energygeneration phase.
Running downhill at a grade of 8.3% increases
negative work done by the ankle extensors from
–13 J in level running to –26 J. Corresponding
values for the knee extensors are –30 J and –58 J,
respectively (Buczek & Cavanagh 1990). Although
muscles do relatively more negative work during
downhill running, it is not clear why downhill
running causes soreness in the leg extensors,
whereas level running with comparable values
of negative work does not (Buczek & Cavanagh
1990).
Running long and vertical jumps
During the stance phase of maximum running long
jumps with the results of 6.1 and 7.0 m, the total negative work done in 15 joints and three orthogonal
planes is – 878 J (or 130% of the total positive work).
From this amount of negative work, – 656 J (or 75%)
is done in the stance leg joints and –119 J (14%) in
the swing leg joints. Most of the negative work of
the stance leg is done in the sagittal plane (94%)
(Prilutsky 1990). Power patterns and work done in
individual joints of the stance leg depend on athlete
techniques and the length of the jump. Examples of
the powers developed in the stance leg joints during
a running long jump are shown in Fig. 4.13 (Tupa
et al. 1980). The ankle and knee extensor muscles
absorb energy during approximately the first half of
the stance, and they generate energy during the rest
of the stance. Peaks of negative and positive power
at the two joints are very high (Fig. 4.13). Note that
peaks of positive power greatly exceed the maximum positive power obtained from the curves of
joint moment and joint velocity, measured in maximum concentric actions (van Ingen Schenau et al.
1985; Prilutsky et al. 1992). This observation supports the notion of the enhancement of positive
power during the SSC. In addition, some of the
power recorded at distal joints may be transferred
there from more proximal joints by two-joint muscles (van Ingen Schenau et al. 1985; Prilutsky &
Zatsiorsky 1994).
eccentric action
Power (W)
2445
0
–2068
4294
0
–16396
5591
77
Hip
Knee
Ankle
0
–2893
Fig. 4.13 Powers developed by moments at the stance (ipsilateral) leg in the sagittal plane during running long jump. The
right horizontal line corresponds to the stance phase of the ipsilateral leg (shown by solid lines on the stick figure); the left
horizontal line corresponds to the stance phase of the contralateral leg (shown by dashed lines on the stick figure). The
length of the ipsilateral stance phase is 0.148 s; the jump length is 7.2 m. (Adapted from Tupa et al. 1980.)
In submaximal running long jumps the amount of
negative work done in the sagittal plane is smaller
than in maximum jumps: –44, –133, –80 and –28 J
for the metatarsophalangeal, ankle, knee and hip
joints, respectively; the corresponding values of
positive work are 2, 104, 52 and 56 J (Stefanyshyn &
Nigg 1998).
Joint power patterns during maximum running
vertical jumps are similar, in general, to those in
the running long jumps (Fig. 4.14). The peak power
values are substantially smaller in the ankle and
the knee. The hip extensors do positive work in the
first half of the stance, and they mostly absorb
energy at the end of the stance phase (Fig. 4.14).
However, the hip power is more variable than
ankle and knee power in running vertical and long
jumps (Stefanyshyn & Nigg 1998). The amounts
of negative and positive work done by the extensors of the major leg joints are smaller, in general,
during running vertical jumps than during running
long jumps (Tupa et al. 1980; Stefanyshyn & Nigg
1998).
In standing countermovement vertical and long
jumps, the ankle, knee and hip extensors absorb
energy of the body to stop the countermovement,
and then they generate energy to accelerate the
Hip
2224
0
Power (W)
–1111
1567
Knee
0
–3976
781
0
–782
Ankle
Fig. 4.14 Powers developed by moments at the stance (contralateral) leg in the sagittal plane during running vertical
jump. The right horizontal line corresponds to the stance phase of the contralateral leg (shown by dashed lines on the stick
figure); the left horizontal line corresponds to the stance phase of the ipsilateral leg (shown by solid lines on the stick
figure). The duration of the contralateral stance phase is 0.224 s; the result of the jump is 1.85 m. (Adapted from Tupa et al.
1980.)
78
muscle action in sport and exercise
body (Horita et al. 1991; Anderson & Pandy 1993).
Despite the fact that the leg extensors experience the
SSC and the results of the countermovement jumps
are consistently better than squat jumps, where the
muscles do not absorb energy prior to the push-off
phase (Prilutsky 1990; Bobbert et al. 1996), it does not
appear that the conditions for the enhancement of
positive work due to the preliminary muscle stretch
are met in the countermovement jumps. In two computer simulation studies by Anderson and Pandy
(1993) and Bobbert et al. (1996), the authors demonstrated that elastic energy stored in the muscles
prior to the push-off phase was nearly the same in
the two types of jump. Bobbert et al. (1996) explain a
better performance of the countermovement jump
compared with the squat jump by a higher muscle
force developed at the beginning of the push-off
phase in the countermovement jump than in the
squat jump. However, since most of the elastic
energy in the countermovement jump comes from
the decrease in potential energy of the body, and
in the squat jump, from work done by the muscle
contractile elements on the SEC (Anderson & Pandy
1993), the countermovement jump seems to require
less metabolic energy per unit of positive work
than the squat jump (Anderson & Pandy 1993; see
also ‘Economy and efficiency of positive work’
above).
Landing
During landings from heights of 0.32–1.28 m, the leg
joint moments (leg extensors) do primarily negative
work (Prilutsky 1990; DeVita & Skelly 1992; McNittGray 1993; Prilutsky & Zatsiorsky 1994). The
amount of work, the relative contribution of different joints to the total work, and patterns of joint
powers depend substantially on whether the landing is soft or stiff. In a very soft landing after a jump
from 0.5 m (where nearly the entire decrease in the
total energy of the body is dissipated by the joint
moments (see ‘Dissipation of mechanical energy’
above), the total negative work done by the leg
joints is –592 J; and the ankle, knee and hip moments
absorb –159, –248 and –185 J (Prilutsky 1990). In
more stiff jumps (where a substantial portion of the
body energy is dissipated in the passive anatomical
structures (see ‘Dissipation of mechanical energy’
above), the negative work done in the joints is typically less (Prilutsky 1990; DeVita & Skelly 1992).
Examples of power developed during soft and stiff
landings at three leg joints are shown in Fig. 4.15.
Peaks of negative power, which are typically greater
in stiff landings, can reach –30 to –40 W per unit
body mass for landings from 0.32 to 0.59 m, and
–150 W per unit body mass for landings from 1.28 m
(DeVita & Skelly 1992; McNitt-Gray 1993). For more
information about the biomechanics of landing, see
Chapter 25.
Cycling
Power and work produced by ankle, knee and hip
moments during cycling increase with resistance
power and pedalling rate (Fig. 4.16). Most of the
work done by the leg moments is positive. For
example, according to Ericson (1988), at a resistance
power of 120 W and pedalling rate of 60 r.p.m., the
total positive work done by moments of one leg in
the cycle is 67 J, whereas the corresponding negative work is only –6 J (9%). At a resistance power of
240 W and the same pedalling rate, the values of
positive and negative work are 126 J and –7 J (6%),
respectively. Almost each major leg muscle acts
eccentrically in short periods of the pedal revolution
when muscle elongation coincides with the development of muscle forces (Hull & Hawkins 1990;
Gregor et al. 1991). However, the amount of negative work done by the muscles in cycling is probably
small.
Thus, the assumption accepted by many researchers that in normal cycling muscles do primarily positive work seems to be justified.
Acknowledgements
The preparation of this chapter was supported in
part by a grant from the Office of Interdisciplinary
Programs at Georgia Institute of Technology to the
Center for Human Movement Studies (director,
Professor Robert J. Gregor). The author thanks Mark
A. Broberg for his help in editing the English.
eccentric action
79
20
Hip
10
0
–10
–20
–30
20
Knee
Soft
Power (W · kg–1)
10
0
–10
–20
–30
20
Ankle
10
Stiff
0
Soft
–10
–20
Stiff
–30
–100 –50
(a)
(b)
0
50
100
150
200
250
300
350
400
Time (ms)
Fig. 4.15 (a) Stick figure representations of typical soft and stiff landings. The stiff landing had a more erect body posture
through the landing. (b) Joint power curves normalized to body mass in the sagittal plane from representative soft and
stiff landings. Negative and positive times indicate descent and floor contact phases. (From DeVita & Skelly 1992.)
80
muscle action in sport and exercise
Hip
250
A
150
100
50
B
0
–50
A
40 r.p.m.
60 r.p.m.
80 r.p.m.
100 r.p.m.
150
Muscular power (W)
Muscular power (W)
200
Hip
200
0W
120 W
240 W
100
B
50
0
–50
90
0
180
270
–100
360
0
90
Crank angle (degrees)
Knee
250
Muscular power (W)
Muscular power (W)
200
150
100
D
50
0
–50
0
90
180
270
100
360
270
360
D
50
–50
360
0
90
180
Crank angle (degrees)
Ankle
Ankle
250
200
Muscular power (W)
200
Muscular power (W)
270
150
0
250
150
E
100
50
0
(a)
360
C
Crank angle (degrees)
–50
270
Knee
250
C
200
180
Crank angle (degrees)
150
E
100
50
0
0
90
180
Crank angle (degrees)
270
–50
360
(b)
0
90
180
Crank angle (degrees)
Fig. 4.16 Powers of joint moments in the sagittal plane during cycling: 0 and 360° crank angles correspond to pedal top
position, and 180° crank angle to pedal bottom position. A, Positive hip extensor power; B, positive hip flexor power;
C, positive knee extensor power; D, positive knee flexor power; E, positive ankle extensor power. (a) Cycling at different
resistance powers (0, 120 and 240 W). (b) Cycling at different pedalling rates (40, 60, 80 and 100 r.p.m.) against the same
resistance giving power outputs of 80, 120, 160 and 200 W, respectively. (From Ericson 1988; Figs 1 & 2.)
eccentric action
81
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during knee extensor contractions.
Medicine and Science in Sports and Exercise
23, 1187–1193.
Wassermann, K., Hansen, J.E., Sue, D.Y. &
Whipp, B.J. (1986) Principles of Exercise
Testing and Interpretation. Lea & Febiger,
Philadelphia.
Wells, R.P. (1988) Mechanical energy costs
of human movement: an approach to
evaluating the transfer possibilities of
two-joint muscles. Journal of Biomechanics
21, 955 –964.
Westing, S.H., Seger, J.Y. & Thorstensson,
A. (1990) Effects of electrical stimulation
on eccentric and concentric torquevelocity relationships during knee
extension in man. Acta Physiologica
Scandinavica 140, 17–22.
Westing, S.H., Cresswell, A.G. &
Thorstensson, A. (1991) Muscle
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eccentric and concentric extension.
European Journal of Applied Physiology 62,
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Whipp, B.J. & Wasserman, K. (1969)
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Winter, D.A. (1983a) Energy generation
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Clinical Orthopaedics and Related Research
175, 147–154.
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Winter, D.A. (1983b) Moments of force and
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Biomechanics 13, 476–479.
Woledge, R.C., Curtin, N.A. & Homsher, E.
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Chapter 5
Stretch–Shortening Cycle of Muscle Function
P.V. KOMI AND C. NICOL
Introduction
Traditionally muscular exercises have been classified into static and dynamic types. However, even
if this classification is further extended into isolated
forms of isometric, concentric and eccentric muscle
actions, it does not correctly describe the true nature
of muscle function and its forms of contraction.
Muscular exercises seldom, if ever, involve pure
forms of isolated contraction types. This is because
the body segments are periodically subjected to
impact or stretch forces. Running, walking and hopping are typical examples of how external forces
(e.g. gravity) lengthen the muscle. In this particular
phase the muscle is acting eccentrically, and concentric (shortening) action follows. According to the
definition of eccentric action, the muscles must be
active during stretch. This combination of eccentric
and concentric actions forms a natural type of
muscle function called the stretch–shortening cycle,
or SSC (Norman & Komi 1979; Komi 1984, 1992)
(Fig. 5.1).
A particularly important feature of the SSC is
that the muscles are preactivated before they are
subjected to stretch (eccentric actions). SSC muscle
function has a well-recognized purpose: enhancement of performance of the final phase (concentric
action) when compared with the isolated action (e.g.
Komi 1984). This can be demonstrated in isolated
muscle preparations with constant electrical stimulation (e.g. Cavagna et al. 1965, 1968), in animal
experiments with natural and variable muscle
Preactivation
Fig. 5.1 In human walking and
running considerable impact loads
occur when contact is made with the
ground. This requires preactivation
of the lower limb extensor muscles
before ground contact to prepare
them to resist the impact (a) and the
active braking (stretch) phase
(b). The stretch phase is followed
by a shortening (concentric) action
(c). (After Komi 1992.)
(a)
Stretch
(b)
Shortening
(c)
87
88
muscle action in sport and exercise
90°
90°
0.9s
175°
175°
+
175°
–
+
Concentric
Eccentric
Concentric Eccentric
(Long delay)
(a)
+
–
Pure
concentric
(No delay)
(b)
activation (e.g. Gregor et al. 1988), and in maximal
effort conditions of human SSC actions (Cavagna et
al. 1968; Komi 1983). Figure 5.2 demonstrates the
force potentiation in SSC in humans where the
coupling between the stretch and shortening is
varied. Since Cavagna et al. (1965) introduced the
basic mechanisms of work enhancement when an
isolated muscle was subjected to active stretch
(eccentric action) prior to its shortening (concentric
action), considerable scientific work has been devoted to explain the detailed mechanisms of force
and power potentiation in SSC. Cavagna et al. (1965)
argued that this enhancement is primarily elastic
in nature, and although many additional alternative explanations (e.g. Huijing 1992; Komi &
Gollhofer 1997; van Ingen-Schenau et al. 1997)
have been given, no convincing evidence has been
presented to refute the notion that elastic potentiation plays an important role in force potentiation
during SSC.
At the level of a single muscle group, SSC can be
demonstrated well by using direct in vivo tendon
force measurements, for example during running.
The technique used to obtain the Achilles tendon
(AT) force curves of Fig. 5.3 involved implanta-
(c)
Fig. 5.2 Demonstration of the
importance of the short coupling time
between eccentric and concentric
phases for performance potentiation
in the concentric phase of SSC.
(a) Longer delay (0.9 s) was allowed
between the eccentric and concentric
phases. The potentiation effect on the
concentric phase was reduced.
(b) Concentric action is preceded by
eccentric (–) action, but no delay is
allowed when contraction type is
changed from stretch to shortening.
The eccentric (stretch) phase begins
in the middle of the movement from
the 175° (knee in an extended
position) to the 90° position. Note the
clear force potentiation in the
concentric phase (+) compared with
the condition on the right. (c) Pure
concentric contraction of the knee
extension from 100° to 175°. (From
Komi 1983.)
tion of a buckle transducer under local anaesthesia
around the AT of a healthy human subject (Komi
1990). This technique allowed the subject to perform unrestricted locomotion, including walking,
running at different speeds, hopping, jumping and
bicycling. In some cases even maximal long jumps
were performed without any discomfort. Figure 5.3
presents typical results of the occurrence of SSC in
gastrocnemius and soleus muscles during running
at moderate speed. There are several important features to be noted in Fig. 5.3. First the changes in
muscle-tendon length are very small (6 –7%) during
the stretching phase. This suggests that the conditions favour the potential utilization of short-range
elastic stiffness (SRES) (Rack & Westbury 1974) in
the skeletal muscle. Various length changes are
reported in the literature demonstrating that the
effective range of SRES in in vitro preparations is
1– 4% (e.g. Huxley & Simmons 1971; Ford et al.
1978). In the intact muscle-tendon complex in vivo,
this value is increased because series elasticity and
fibre geometry must be taken into account. This
could then bring the muscle-tendon lengthening
to 6 –8%. Other findings, in addition to that of
Fig. 5.3, indicate that length changes of the triceps
stretch—shortening cycle
89
1 mV
M. tibialis
anterior
1 mV
M. gastrocnemius
1 mV
M. soleus
0
%
Fig. 5.3 Demonstration of SSC for the
triceps surae muscle during the
(functional) ground contact phase of
human running. Top: Schematic
representing the three phases of SSC
presented in Fig. 5.1. The remaining
curves represent parameters in the
following order (from the top):
rectified surface EMG records of the
tibialis anterior, gastrocnemius and
soleus muscles; segmental length
changes of the two plantar flexor
muscles; vertical ground reaction
force; directly recorded Achilles
tendon force; and the horizontal
ground reaction force. The vertical
lines signify the beginning of the
foot (ball) contact on the force plate
and the end of the braking phase,
respectively. The subject was running
at moderate speed. (From Komi
1992.)
Segment
length (∆%)
10
250 N
Vertical force
250 N
Achilles tendon
tension
100 N
Horizontal force
100 ms
90
muscle action in sport and exercise
surae-Achilles tendon complex are, in running and
drop jumps, between 6 and 9% during the functional contact phase. When measurements are made
on the muscle fibre level, the values are naturally
smaller, as shown by Roberts et al. (1997) in turkeys
running on level ground.
The second important feature in Fig. 5.3 is that the
segmental length changes in these two muscles
(gastrocnemius and soleus) take place in phase in
both the lengthening and shortening parts of SSC.
This is typical for running and jumping, and it has
considerable importance because the buckle transducer measures forces of the common tendon for
the two muscles. The situation is not so simple in
some other activities, such as bicycling (Gregor et al.
1991), where the length changes are more out of
phase in these two muscles. The third important
feature of the example in Fig. 5.3 is that the form
of the AT force curve resembles that of a bouncing
ball, implying efficient force potentiation.
Muscle mechanics and performance
potentiation in SSC
The true nature of force potentiation during SSC
can be seen by computing the instantaneous force–
length and force–velocity curves from the parameters shown in Fig. 5.3. Figure 5.4 presents the results
of such an analysis from fast running; it covers the
functional ground contact phase only. It is important to note from this figure that the force–length
curve demonstrates a very sharp increase in force
during the stretching phase, which is characterized
by a very small change in muscle length. The righthand side of the figure shows the computed instantaneous force–velocity comparison suggesting high
potentiation during the shortening phase (concentric action). Figure 5.5, on the other hand, represents
examples of electromyographic (EMG)–length and
EMG–velocity plots for moderate running. It clearly
demonstrates that muscle activation levels are variable and primarily concentrated for the eccentric
part of the cycle. This is important to consider when
comparing the naturally occurring SSC actions with
those obtained with isolated muscle preparations
and constant activation levels throughout the
cycle.
The force–velocity curve of Fig. 5.4 is a dramatic
demonstration that the instantaneous force–velocity
curves are very unlike the classical curve obtained
for the pure concentric action with isolated muscle
preparations (e.g. Hill 1938) or with human forearm
10
8
8
6
4
Tendon force (kN)
10
6
4
2
–10
–8
–6
–4
–2
Length (Ga) (%)
0
2
2
–1.5
–1
–0.5
0
0.5
1
1.5
Velocity
Fig. 5.4 Instantaneous force–length and force–velocity curves of the gastrocnemius muscle for SSC when the subject
ran at fast speed (9 m · s–1). The upward deflection signifies stretching (eccentric action) and the downward deflection
shortening (concentric action) of the muscle during ground contact. The horizontal axes have been derived from
segmental length changes according to Grieve et al. (1978). (From Komi 1992.)
2
stretch—shortening cycle
0.3
0.2
0.2
0.1
–12
–9
–5
EMG (Sol) (mV)
0.3
–3
91
0.1
–2.5
–1.5
–0.5
Length (So) (%)
0.5
1.5
2.5
Velocity
Fig. 5.5 Instantaneous EMG–length and EMG–velocity curves of the soleus muscle for SSC when the subject ran at
moderate speed. The arrows indicate how the events changed from stretching to shortening during the contact phase.
Please note that the EMG activity is primarily concentrated in the eccentric part of the cycle.
Figure 5.6 shows the instantaneous plots of the
force–velocity curve during hopping. The classical
type of curve obtained with constant maximal
activation for the concentric action of the triceps
surae is superimposed in the same graph. The area
between the two curves suggests remarkable force
potentiation in the concentric part of SSC.
The in vivo measurement technique for humans
has been developed following reports on animal
experiments (e.g. Sherif et al. 1983). Many of these
animal studies have included similar parameters to
ATF (kN)
flexors (e.g. Wilkie 1950; Komi 1973). Although Fig.
5.4 does not present directly the comparison of the
force–velocity (F–V) curve for the final concentric
(push-off) phase with the classical curve, it certainly
suggests considerable force potentiation. Unfortunately the human experiment shown in Fig. 5.4 did
not include comparative records obtained in a
classical way. However, our recent development of
in vivo measurements with an optic-fibre technique
(Komi et al. 1995) has now been utilized to obtain
these comparisons.
Fig. 5.6 Instantaneous force–velocity
curve of the gastrocnemius muscle
for the ground-contact phase of
hopping. Note that in the concentric
phase the force is greater (shaded
area) than that of the force–velocity
curve measured in the classical way.
The data were obtained with the
optic-fibre technique (Komi et al.
1996) of Achilles tendon force
recordings. (From Finni et al. in
preparation.)
4
3
2
Hopping
1
–0.4
–0.2
0
0.2
Velocity (m · s–1)
0.4
0.6
92
muscle action in sport and exercise
those used in our human studies, such as muscle
length, force and EMG. The most relevant report
for comparison with present human experiments is
that of Gregor et al. (1988); these authors measured
the mechanical outputs of the cat soleus muscle
during treadmill locomotion. In that study the
results indicated that the force generated at a given
shortening velocity during the late stance phase was
greater, especially at higher speeds of locomotion,
than the output generated at the same shortening
velocity in situ. Thus, both animal and human in vivo
force experiments seem to give similar results with
regard to the force–velocity relationships during
SSC.
The difference between the force–velocity curve
and the classical curve in isolated muscle preparations (e.g. Hill 1938) or in human experiments (e.g.
Wilkie 1950; Komi 1973) may be partly due to natural differences in muscle activation levels between
the two types of activities. While the in situ preparations may primarily measure the shortening properties of the contractile elements in the muscle, natural
locomotion, primarily utilizing SSC action, involves
controlled release of high forces, caused primarily
by the eccentric action. This high force favours storage of elastic strain energy in the muscle-tendon
complex. A portion of this stored energy can be
recovered during the subsequent shortening phase
and used for performance potentiation. Both animal
and human experiments seem therefore to agree
that natural locomotion with primarily SSC muscle
action may produce muscle outputs which can be
very different to those of isolated preparations,
where activation levels are held constant and storage of strain energy is limited.
The SSC enables the triceps surae muscle to
perform very efficiently in activities such as walking, running and hopping. Recent evidence has
demonstrated that the gastrocnemius and soleus
muscles also function in bicycling in SSC, although
the active stretching phases are not so apparent
as in running or jumping (Gregor et al. 1987, 1991).
In contrast to hopping the elastic recoil of the
triceps surae muscle plays a much smaller role in
countermovement jumps (CMJ) (Fukashiro et al.
1993; Finni et al. 1998). This is expected because in
CMJ the stretch phase is slow and the reflex contribution to SSC potentiation is likely to be much
less than in hopping.
Role of stretch reflexes in force
enhancement during SSC
When discussing the possible reflex mechanisms
involved in performance potentiation during SSC,
the key question is what are the important features
of effective SSC function. In our understanding an
effective SSC requires three fundamental conditions
(Komi & Gollhofer 1997):
1 well-timed preactivation of the muscle(s) before
the eccentric phase;
2 a short fast eccentric phase; and
3 immediate transition (short delay) between
stretch (eccentric) and shortening (concentric)
phases.
These conditions are well met in ‘normal’ activities such as running and hopping, and seem therefore suitable for possible interaction with stretch
reflexes.
Demonstration of short latency stretch reflexes
in SSC
Stiffness regulation is a very important concept
in the eccentric part of SSC, and stretch reflexes play
an important role in this task. Hoffer and Andreassen (1981) demonstrated convincingly that when
reflexes are intact, muscle stiffness is greater for the
same operating force than in an arreflexive muscle.
Thus, stretch reflexes may already make a net contribution to muscle stiffness during the eccentric
part of SSC.
In hopping and running, the short-latency
stretch reflex component (SLC) can be quite easily
observed, especially in the soleus muscle. Figure 5.7
illustrates studies where this component appears
clearly in the EMG patterns when averaged over
several trials involving two leg hops with short
contact times. Also Voigt et al. (1997), in a similar
study, measured both the origin-to-insertion muscle
lengthening and the muscle fibre lengthening. Both
measurements showed high stretch velocities in
stretch—shortening cycle
93
Magnitude of reflex-induced EMG activity
Both legs
0.5mV
Sol
0.5mV
Ga
0.5mV
VM
100
Fz
100ms
Fig. 5.7 Averaged rectified EMG records of the soleus
(Sol), gastrocnemius (Ga), and vastus medialis (VM)
muscles in the drop jump from 60 cm height. Note the
sharp EMG reflex peak in the soleus muscle during early
contact phase. (Reprinted, by permission, from Komi &
Gollhofer 1997.) (After Gollhofer et al. 1992.)
the early contact phase, which led the authors to
conclude that the conditions were sufficient for
muscle-spindle afferent activation. The SLC is sensitive to loading conditions as shown in Fig. 5.8,
where the stretch loads vary from the preferred submaximal hopping (the records on the top) to drop
jumps. In the highest drop jump condition (80 cm)
the SLC component becomes less clear, suggesting
decreased facilitation from the muscle spindles
and/or increased inhibitory drive from various
sources (e.g. Golgi tendon organ (GTO), voluntary
protection mechanisms, etc.). In cases where the
drop jumps have been performed from excessive
heights, for example from 140 cm (Kyröläinen &
Komi 1995), the subjects had to sustain extreme
loads during contact. In these situations, the reduced reflex activation may functionally serve as
a protection strategy to prevent muscle and/or
tendon injury.
It has been shown during passive dorsiflexion tests
that the SLC and the medium latency component
(MLC) can be dramatically reduced if the measurements are made during ischaemic blockade of the
lower limb (e.g. Fellows et al. 1993). This method has
been applied to conditions of fast running (Dietz
et al. 1979), in which the control runs made before
ischaemia demonstrated that the gastrocnemius
EMG had a clear SLC component during contact.
The average peak EMG was at least two times
higher than that measured during a maximal voluntary isometric plantar flexion test (Fig. 5.9). When
ischaemic blockade was performed, the gastrocnemius EMG during contact was dramatically
reduced in the fast running test with the same
velocity, but there was no change in preactivation.
These results emphasize the potential role of Ia
afferent input in SSC-type activities such as running. The ischaemic blockade is used to isolate the
Ia afferent information acting on spinal pathways
(Fellows et al. 1993).
Do reflexes have time to be operative during
SSC?
As it has been reportedly questioned and denied
that stretch reflexes can operate and contribute
to force and power enhancement during SSC
(van Ingen-Schenau et al. 1997), it is important to
examine what role the stretch reflexes may play,
if any, during SSC. It is difficult to imagine that
proprioceptive reflexes, the existence of which has
been known for centuries, would not play any
significant role in human locomotion including
SSCs. It is true that in normal movements with
high EMG activity, the magnitude and net contribution of reflex regulation of muscle force
are methodologically difficult to assess. The task
becomes much easier when one studies relatively
slow (1.2–1.9 rad · s–1) passive dorsiflexions, where
the stretch-induced reflex EMG has been reported
to enhance AT force by 200 –500% over the purely
passive stretch without reflex EMG response
(Nicol & Komi 1998). Figure 5.10 is an example of
94
muscle action in sport and exercise
Soleus EMG
BLH
0.5mV
20cm
40cm
60cm
2.5 kN
0.25 mV
80cm
100ms
Fast running
Normal
Ischaemia
Max
ISOM
EMG
Contact
100ms
Contact
Fig. 5.8 Rectified and averaged
EMG-pattern of the soleus muscle
and vertical ground reaction force in
various stretch–shortening cycle
drop jumps with both legs. The figure
illustrates the modulation in the
pattern and in the force record with
increasing stretch load. From top: BLH
(both legs hopping in place), and
20–80 cm (drop jumps from 20 to
80 cm height, landing with both legs).
The dashed vertical line indicates the
initiation of the phasic activation
with a latency of 40 ms after ground
contact. (Reprinted, by permission,
from Komi & Gollhofer 1997.)
Fig. 5.9 Rectified and averaged EMG
activity of the gastrocnemius muscle
when the subject was making many
steps during fast running on the
spot. The control (normal) before
ischaemia shows the typical rapid
increase of EMG 40 ms after ground
contact. The dashed line indicates
the same running after 20 min of
ischaemia produced by a tourniquet
around the thigh. The stretchinduced EMG activity (SLC
component) was reduced to the
level of Max iISOM EMG (the bar
on the right) without reduction in
the preactivity before contact.
(After Dietz et al. 1979.)
stretch—shortening cycle
Stretch at 0.44rad·s–1
(N)
300
Stretch at 1.2 rad · s–1
(N)
300
150
150
ATF
0
ATF
0
EMGs
EMGs
0.04
0.04
Pedal
0.08
(rad)
95
0.08
20ms
(a)
Pedal
20 ms
(rad)
(b)
Fig. 5.10 Demonstration of passively induced stretch reflexes on the Achilles tendon force (ATF). (a) Passive dorsiflexion
at slow stretch caused no reflex EMG response and led to a small and rather linear increase of the ATF (purely passive
response). (b) With faster and larger stretches the reflex contribution to ATF corresponds to the additional ATF response
above the purely passive influence represented by the dashed line. (From Nicol & Komi 1998.)
these measurements and it shows a typical delay of
12–13 ms between the onset of reflex EMG and onset
of force potentiation.
This time delay is similar to electrical stimulation
measurements performed together with fibre-optic
recordings of the AT force (Komi et al. manuscript in
preparation). Considering the duration of the simple stretch reflex loop of 40 ms, the maximum delay
between initial stretch and subsequent force potentiation would be around 50–55 ms. When referred
to running the first contact on the ground would
indicate the point of initial stretch. In marathon running the contact phase usually lasts almost 250 ms
implying that this reflex-induced force enhancement would already have functional significance
during the eccentric phase of the cycle (Nicol et al.
1991c). As the contact phase duration (braking and
push-off) decreases as a function of the running
speed (Luhtanen & Komi 1978) the net reflex contribution will occur at the end of the eccentric phase
at faster speeds, and may be extended partly to the
push-off phase in maximal sprinting, where the
total contact time is only about 90–100 ms (Mero
& Komi 1985). These time calculations certainly
confirm that stretch reflexes have ample time to
operate for force and power enhancement during
SSC, and in most cases during the eccentric part
of the cycle. Thus, there are no time restraints
for reflexes to be operative in stiffness regulation
during SSC. The large reflex-induced EMG component (see Fig. 5.9) must therefore be regarded as an
essential and important contribution to force
enhancement in SSC.
Functional significance of stretch reflexes
in SSC activities
Some aspects of the functional importance of stretch
reflexes during SSC have already been referred to
above. It is, however, relevant to emphasize that the
reflexes contribute to the efficiency of the motor
output by making the force output more powerful.
In SSC this can only be accomplished by an immediate and smooth transfer from the preactivated and
eccentrically stretched muscle-tendon complex to
the concentric push-off, in the case of running or
hopping, for example. The range of high stiffness is,
however, limited to that of the ‘short-range elastic
stiffness’ (SRES) (Rack & Westbury 1974; Morgan
1977). In this case the stiffness of the muscle-tendon
complex depends not only on the range of motion
(Kearney & Hunter 1982), but also on the efficiency
of the stretch reflex system (Nichols & Houk 1976;
Houk & Rymer 1981). High stretch-reflex activity
is expected after a powerful stretch of an active
muscle (e.g. Dietz et al. 1984), and these reflexes
are necessary not primarily to enhance SRES, but to
linearize the stress-strain characteristics (Nichols
96
muscle action in sport and exercise
1974; Hufschmidt & Schwaller 1987).
It can be assumed that before ground contact in
SSC the initial lengthening of the muscle-tendon
complex, shown in Fig. 5.3, occurs in the more or
less compliant Achilles tendon. As soon as the ‘critical’ tension is achieved, which is determined by the
amount of activity (preactivation) sent to the muscles prior to contact, the forceful ‘yielding’ of the
cross-links of the acto-myosin complex may take
place, with concomitant loss of the potential energy
stored in the lengthened cross-bridges (e.g. Flitney
& Hirst 1978). From in vitro studies it is known that
yielding of active cross-bridges can be prevented by
intense muscular activation. Such an intense phasedependent and triggered muscular activation can
be provided most effectively by the stretch reflex
system, which is highly sensitive to the length and
tension changes in the muscle-tendon complex.
As discussed earlier, the latencies for the reflex
EMG are sufficiently short for it to have functional
significance. These latencies (40–45 and 12–14 ms,
respectively, for the reflex loop and electromechanical delay) fit well with the occurrence of short- and
medium-latency stretch-reflex components (e.g. Lee
& Tatton 1982). Our recent data on combined stretch
and reflex potentiation are well in agreement with
the SRES concept, demonstrating that the crossbridge force resistance to stretch is particularly
efficient during the early part of the cross-bridge
attachment (Nicol & Komi 1998). Therefore, the
reflex-induced cross-link formation appears to play
a very rapid and substantial role in force generation
during stretch. Furthermore, as demonstrated by
Stein (1982) and Nichols (1987), it is the stretch reflex
system that provides high linearity in muscular
stiffness. All these aspects may contribute to the
observation that mechanical efficiency in natural
SSC is higher than that in pure concentric exercise
(e.g. Aura & Komi 1986; Kyröläinen et al. 1990). The
concept of elastic storage favours the existence of
reflex activation, and high muscular activation during the eccentric phase of SSC is a prerequisite for
efficient storage of elastic energy. Animal studies
have shown that an electrically stimulated muscle
responds to ramp stretches with linear tension
increments, provided the muscle has an intact reflex
system (Nichols & Houk 1976; Nichols 1987). This
linearity is restricted to small length changes (e.g.
Hoffer & Andreassen 1981) and these small changes
are indeed relevant to the SSC exercises referred to
in the present discussion (see also Fig. 5.3).
Overall there seems to be enough evidence to
conclude that stretch reflexes play an important
role in SSC and contribute to force generation
during touchdown in activities such as running
and hopping. Depending on the type of hopping,
for example, the amplitude of the SLC peak and
its force-increasing potential may vary considerably. However, the combination of the ‘prereflex’
background activation and the following reflex
activation might represent a scenario that supports yield compensation and a fast rate of force
development (Voigt et al. 1997). This scenario may
be especially effective in a non-fatigued situation,
but it can be put under severe stress during SSC
fatigue.
Fatigue effects of SSC exercise
Mechanical effects
There are several models for studying exhausting
SSC exercise, but they have all given remarkably
similar results. A special sledge ergometer developed in our laboratory (Kaneko et al. 1984; Komi
et al. 1987) has been used to perform short-term
SSC fatigue in either arm (Gollhofer et al. 1987) or
leg muscles (Horita et al. 1996; Nicol et al. 1996).
Another possibility is to use long-lasting exercise,
such as marathon running, as the SSC fatigue model
(e.g. Avela et al. 1999a). In these different studies, the
immediate changes in mechanical performance
reveal clear loss of tolerance to the imposed stretch
loads. Figure 5.11 is an example of the arm exercise
(Gollhofer et al. 1987), in which the repeated 100
SSCs were characterized by progressive increases
in the contact time in both braking and push-off
phases. More specifically, however, progressive
increases in the initial force peak and in the subsequent drop were observed. This phenomenon is
similar to that depicted in Fig. 5.8, in which the
magnitude of both the impact peak and the subsequent drop was higher with higher dropping
height. In the example of Fig. 5.11 the dropping
stretch—shortening cycle
97
Submaximal force
1–10
11–20
21–30
31–40
41–50
51–60
61–70
71–80
81–90
91–100
height was naturally kept constant, but the subject’s
ability to tolerate the same stretch load deteriorated
considerably with fatigue.
The ‘marathon-run’ model has also shown similar
changes in the ground contact force parameters,
either in submaximal running tests (Komi et al. 1986)
or in tests also including submaximal and maximal
SSC tests (Nicol et al. 1991a,c). Figure 5.12 is a representative example of such a result, which has
been confirmed in subsequent tests with similar
marathon-run models (Avela et al. 1999). Kinematic
analysis has revealed that, both in the short-term
100 ms
exercise (Gollhofer et al. 1987; Horita et al. 1996) and
long-term SSC fatigue (Nicol et al. 1991a), these
ground reaction force changes are associated with
problems in maintaining a constant angular displacement during contact when fatigue progresses.
In a fatigued state the reduction in the force after the
impact is likely to be related to the observed faster
and longer flexion movement (Nicol et al. 1991c;
Horita et al. 1996). In the case of the arm exercises the
dramatic increase in the impact peak results most
likely from increased preactivity of the arm extensors, as suggested by Gollhofer et al. (1987). The
Sprint run test
Before
After
marathon
Fz
Heel
contact
(a)
Knee angle (degrees)
Fig. 5.11 Fatiguing arm SSC exercise
resulted in progressive changes in the
reaction force record during hand
contact with the sledge force plate.
The records have been averaged for
groups of 10 successive force–time
curves. Note the increase in the
impact peak with subsequent
increase in the force reduction when
fatigue progressed. (Adapted from
Gollhofer et al. 1987.)
Toe-off
Vertical ground reaction force–time curve
(b)
Flex.
80
140
Ext. Heel contact
Flex.
140
Toe-off
200
Ext.
Hip angle (degrees)
Fig. 5.12 The influence of a marathon run on (a) the vertical ground reaction force and (b) the knee/hip angle diagram.
Note a sharp drop in the peak of the sprint force–time curve (a) after the marathon. The angle/angle diagram (b) shows a
greater knee flexion immediately after the heel contact in the post-marathon situation. (After Nicol et al. 1991a,c.)
98
muscle action in sport and exercise
decrease in force after impact is, however, probably
the main indicator of a reduction in tolerance to
repeated stretch loads as fatigue progresses. A logical consequence of this is that in order to maintain
the same SSC performance, for example a constant
marathon speed, the subject must perform greater
work during the push-off phases leading to even
faster progression of fatigue.
The mechanical effects of the fatiguing SSC exercise also have long-lasting consequences, which are
in many ways similar to purely eccentric exercise.
The eccentric fatigue has, however, been referred to
more extensively in earlier reviews (e.g. Komi &
Nicol 2000; Clarkson et al. 1992), and will therefore
not be discussed here in any detail.
In the isometric or concentric fatigue exercises
recovery takes place quite rapidly. In SSC exercise,
as in eccentric fatigue, both the performance measures (e.g. static and dynamic maximal force test)
and the ground reaction force parameters have a
recovery phase which may last several days or
weeks. In the case of the marathon run, the delayed
process takes place in parallel between the maximal
EMG activation and maximal force (Fig. 5.13). A
more detailed examination of the recovery processes, especially in the short-term intensive SSC
exercise, indicates that they take place in a bimodal
fashion—showing a dramatic decline immediately
after the exercise followed by a short-lasting recovery and a subsequent secondary drop. This second
decline in performance may peak either around the
MV
aEMG
2000
1500
400
1000
200
500
Marathon
0
Before
After
+2 days +4 days +6 days
0
Fig. 5.13 Competitive marathon running causes a
dramatic reduction and delayed recovery of maximum
EMG and force of the isometric knee extension.
(From Pullinen et al. 1997.)
MV (N)
aEMG (µV)
600
second or third day post-exercise (Nicol et al. 1996;
Avela et al. 1999b; Horita et al. 1999). The immediate reduction in performance is naturally related
mostly to the metabolic disturbances, whereas the
secondary decline must be associated with the wellknown inflammatory processes related to muscle
damage (Faulkner et al. 1993), which is easily
observable after both SSC and eccentric types of
fatigue protocols.
Fatigue effects on the stretch reflex-induced
force production
Since our earlier reviews (Nicol et al. 1996; Komi
& Nicol 2000) considerable evidence has accumulated to indicate that SSC fatigue induces problems in stiffness regulation and that stretch
reflexes are major players in this process. Due to the
limited space available, the present discussion
focuses on the most relevant issues in this regard.
The stretch reflex analysis performed either in the
passive condition (e.g. Nicol et al. 1996) or during
the SSC exercise itself (Horita et al. 1996; Avela &
Komi 1998a,b; Avela et al. 1999b) reveal that the
stretch reflex amplitude (passive condition) or the
short-latency stretch reflex component (SLC) (M1
amplitude in SSC exercise) are reduced dramatically after the exercise, and their recovery follows
the bimodal trend in parallel with the mechanical
parameters. Figure 5.14 shows this parallelism as
a representative example. The recovery processes
are further delayed when the SSC fatigue exercise
is repeated, before full recovery, on days 5 and
10 after the first exercise (Nicol et al. 1994). This
implies that the stiffness regulation needs a long
time to resume its normal state after exhaustive
SSC exercise.
There seems to be enough evidence to suggest
that coupling could exist also between the performance reduction in SSC and the inflammatory
processes resulting from muscle damage. Firstly,
decreases in SSC performance are related to
increases in an indirect plasma marker (creatine
kinase (CK) activity) of muscle damage in the phase
corresponding to the secondary injury of Faulkner
et al. (1993) and shown in Fig. 5.15a. This coupling
concept is further emphasized by Fig. 5.15b, which
mV
0.8
Stretch reflex amplitude
soleus
110deg-1
200deg-1
0.6
M1 aEMG
mV
0.8
VL
Sol
0.6
*
0.4
0.2
0.2
*
*
0.0
*
*
**
0.4
Before
**
After
2h
after
(a)
2 days
after
4 days
after
6 days
after
0.0
Before
After
(b)
*
*
2h
after
Pre-fatigue
N
Before
After
2h
after
0
PFR
2 days
after
2 days
after
4 days
after
6 days
after
Post-fatigue
VL
6 days
after
4 days
after
–400
Sol
–800
–1200
*
*
*
–1600
**
–2000
*
F
(c)
PFR
(d)
200 ms
Fig. 5.14 The bimodal trend of recovery of stretch reflexes and ground reaction force on the force plate. The stretch
reflexes were measured in two different tests in a group of seven runners before and after a marathon run. (a) Mean
changes in the peak-to-peak stretch reflex amplitude of the soleus muscle recorded during 10 mechanically induced
passive dorsiflexions (0.17 rad induced at 1.9 and 3.5 rad · s–1). (b) Mean values (±SD) of average area of the SLC
component (M1 aEMG) of soleus (Sol) and vastus lateralis (VL) muscles. (c) Peak force reduction (PFR) measured during
the standard sledge jump tests. The parameters in (b) and (c) are also shown as pre- and post-marathon comparisons in
(d). Note the coupling in the reduction and recovery between reflex parameters and PFR. (From Avela et al. 1999b.)
+
r=0.99
N=7
P<0.001
CK (∆%)
CK (∆%)
0
r= 0.94
N= 7
P < 0.001
–300
–600
0
–900
–6
(a)
–4
–2
DJ flight time (∆%)
0
+
0
(b)
–20
0
+
+
+
GA at 70° ·s–1 (∆%)
Fig. 5.15 (a) Increase in creatine kinase (CK) activity during the first two days after exhaustive SSC exercise may be
associated with decrease in the drop jump (DJ) performance. (b) A similar association is also possible between the
recovery of CK activity and stretch reflex amplitude as measured between days 2 and 4 post-SSC fatigue. (Adapted from
Nicol et al. 1996.)
100
muscle action in sport and exercise
Descending
pathways
Spinal
cord
Ib
–
Ia
α
III & IV
Hip
Muscle
damage
Reflex
GTO
Stiffness
Knee
Performance
Ankle
Fig. 5.16 Proposed coupling between SSC exerciseinduced muscle damage and performance reduction.
Muscle damage changes stiffness regulation through
changes in the afferent inputs from the muscle spindle,
Golgi tendon organ (GTO) and group III and IV afferent
nerve endings. The events occur in the following order.
1. Due to muscle damage the stretch-reflex sensitivity
decreases. 2. Muscle (and joint) stiffness regulation
becomes disturbed (reduced). 3. The efficiency of SSC
function (performance) decreases. The proposed
mechanism may be even more apparent in the triceps
surae muscle compared with the quadriceps group of the
figure. (After Horita et al. 1999.)
shows that the subsequent reduction in CK activity
between days 2 and 4 post-exercise is also related to
the respective recovery of the peak-to-peak stretch
reflex EMG amplitude of the examined muscle.
This clearly implies that stiffness regulation itself
behaves in a similar manner, as Horita et al. (1996)
have demonstrated that a parallel exists between
the fatigue-induced changes in the stiffness parameters and the short-latency stretch reflex component (SLC).
The coupling concept can be extended also to the
discussion of the mechanisms leading to reduced
stretch-reflex sensitivity during SSC fatigue. In the
case of SSC, however, the observation may not always
be uniform, because the intensity and duration of
SSC exercise plays an important role in fatiguability
of reflex responses (Gollhofer et al. 1987).
Figure 5.16 summarizes our current view of
the possible interactions between muscle damage,
reduced stretch-reflex sensitivity, reduced stiffness
regulation, and deterioration in SSC performance.
Both presynaptic inhibition (III and IV afferent activation and possibly GTO activation), and several
processes of disfacilitation of the alpha motor
neurone pool may be involved in the coupling. As
regards the latter processes (disfacilitation), our current data rule out the possibility of any significant
influence of reduced fusimotor support to the muscle. Instead, however, they strongly suggest that
the muscle spindle could be directly or indirectly
influenced by exhaustive SSC fatigue (Avela et al.
1999a, 2000).
Direct mechanical damage of the intrafusal muscle fibres has been suggested in a previous review
(Komi & Nicol 2000). While intrafusal fibres may
themselves ‘fatigue’ in the same manner as the
extrafusal fibres, the changes observed in the viscous and elastic properties when the triceps surae
muscle was subjected to long-term repeated passive
stretches (Avela et al. 1998a) strongly suggest that
the mechanical stretching of the muscle spindle may
be modified in the case of fatiguing SSC exercise as
well. Exactly what components are involved in this
process has yet to be demonstrated. It has been suggested that deteriorated structural proteins, such as
titin and desmin, play a part in the process of muscle
damage, and their possible role in SSC fatigue has
been discussed (Avela et al. 1999a, 2000; Horita et al.
1999).
stretch—shortening cycle
101
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Journal of Biomechanics 16, 691–701.
Stein, R.B. (1982) What muscle variable(s)
does the nervous system control in limb
movements? The Behavioral and Brain
Sciences 5, 535 –577.
Voight, M., Dyhre-Poulsen, P. & Simonsen,
E.B. (1998) Modulation of short latency
stretch reflexes during human hopping.
Acta Physiologica Scandinavica 163,
181–194.
Wilkie, D.R. (1950) The relation between
force and velocity in human muscle.
Journal of Physiology 110, 249.
Chapter 6
Biomechanical Foundations of Strength
and Power Training
M.C. SIFF
Introduction
The qualities of strength and power are most popularly associated with sports which require the obvious display of impressive muscular performance
such as weightlifting, wrestling and track-and-field
events. Consequently, whenever strength training
was used as a method of supplementary sports
preparation, it was applied most frequently in
these types of ‘strength’ sports and minimally in
those sports in which the role of the cardiovascular
system was stressed at the expense of almost all
other motor qualities.
However, all sports, and indeed all human movements, necessitate the generation of appropriate
levels of strength and power in a variety of different applications and situations, as will be discussed
later. Several factors have contributed to the prolonged reluctance to accept strength training as a
relevant part of the repertoire for preparing all
types of international athlete for the rigours of toplevel competition, in particular the pre-eminence
bestowed by the medical profession on the role of
cardiovascular fitness in cardiac and general wellbeing, the strong scientific focus on metabolic processes as determinants of sporting performance,
and the exaggerated condemnation of strength
training as a cause of musculoskeletal injury,
impaired flexibility and diminished speed of
movement.
Biomechanics, the application of mechanics to
the understanding of the statics and dynamics of
living organisms, appeared to be relegated largely
to the analysis of human movement, the aetiology of
injuries and the design of equipment for training or
competition—an interesting mathematical and computational pursuit playing a somewhat peripheral
role compared with the more overt physiological
processes which underlie human performance. It is
only fairly recently that biomechanics has assumed
a prominent position alongside the more traditionally accepted aspects of exercise science. It is now
recognized throughout the world as an integral part
of exercise science, ergonomics, sports medicine
and orthopaedics, with numerous universities offering undergraduate and postgraduate courses in this
field.
The contribution of biomechanics to enhancing
sporting and industrial efficiency, performance and
safety is now well accepted and it is now being
applied with great vigour in territory that once
seemed largely the preserve of bodybuilders,
powerlifters and weightlifters whose pursuit of
hypertrophy and strength for many years seemed
to be rather irrelevant to other sports.
The reigning belief was—and in some circles still
is—that strength, power and all other motor qualities in a sport can be quite adequately developed by
means of the sport itself, since this approach ensures
that the principle of specificity is exactly adhered to.
Objective
It is the objective of this chapter to apply biomechanics to examine strength and power as motor
qualities, and thereby to show how this knowledge
may be applied in training to optimize strength
and power in a wide range of sporting applications.
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104
muscle action in sport and exercise
The emphasis is on the practical use of this information, i.e. on the value of applied biomechanics,
rather than on the predominantly theoretical aspects
which often fail to reach the coach and athlete.
However, in striving to meet this objective, it does
not ignore the fact that biomechanics, like any other
component of motor action, does not operate in
glorious isolation of the whole gamut of factors
which determine human performance.
Scope of biomechanics
Biomechanics as a discipline in its own right is relatively new, but its methods, principles and equations have been used for many years in many other
applications. In simple terms, biomechanics is that
discipline which borrows mechanics from the world
of physics and applies it to living forms in order to
understand how they function, with many of the
fundamentals in this field being based upon the
work carried out by Isaac Newton. This chapter falls
into the realm of sports biomechanics, which is that
specialization of biomechanics used to analyse how
the human body functions in a wide spectrum of
sporting activities.
The strengths and weaknesses of sports biomechanics, like that of any other scientific discipline, all
lie in the scope and limitations of the paradigms and
models used to understand and dissect activity in
sport. The dominant paradigm is the widespread
use of models which regard the human body as a
physical machine and thereby enable us to invoke
the powerful physical and mathematical methods
which have proved invaluable to the progress of
applied mechanics in general. This has enabled scientists to scrutinize the human body in motion far
beyond the capabilities of even the most skilled
coach and helped sport to refine training methods,
competitive techniques, rehabilitation technology
and sporting equipment to a degree which seemed
the stuff of science fiction less than half a century
ago.
At the same time, many issues remain unresolved
or controversial, which is a major reason why biomechanics needs to be applied to sport within an
integrated framework comprising all possible fields
which relate to the structure and function of the
human organism in physical action (as is the case in
Russia and much of Europe, the word ‘organism’ is
used in preference to ‘body’, since it refers to all
physical and mental aspects of the living human).
Sporting prowess cannot be explained in terms of
biomechanics, physiology, motor control, psychology or any single one of the other factors which
have become important specializations in the broad
field of sports science. Instead, this prowess has to
be considered as the result of the synergy of every
one of these components acting in a given sport
in a given situation for a given individual at any
given time. Therefore, although the scope of this
chapter lies solidly within the realm of biomechanics, it draws on other relevant components
wherever this may be necessary in the interests of
providing greater completeness.
In particular, neural processes are a superordinate feature of the biomechanics of strength and
power, since they constitute the cybernetic command system which orchestrates the production
of human movement. Thus, while it may appear
adequate to apply analytical mechanistic methods
such as free body diagrams for certain aspects of
understanding sporting movement, it is also necessary to comprehend any implications and limitations of this approach in the context of overall
control mediated by bioelectrical messages passing
between the musculoskeletal and nervous systems
of the body. In many respects, relying solely on
the methods of biomechanics to analyse human
movement is tantamount to analysing a symphony
concert by focusing entirely on the resulting sound
and the musical instruments involved and ignoring
the players and conductor.
For example, it is inadequate to assess the speed
and power of athletes by relying entirely on meticulous force plate and high speed video laboratory
tests or special field tests without examining the
underlying motor control processes. Performance
capabilities suggested by outstanding vertical jumps,
broad jumps or various agility drills are relatively
meaningless if the athlete reacts slowly or inappropriately to sensory stimuli occurring during actual
sporting conditions. This is one of the reasons why
so-called ‘plyometric’ or stretch-shortening drills
may be of little significant benefit to any athlete.
strength and power training
While these drills may improve speed and power in
simple movements, they do not necessarily enhance
reaction time, decision time or problem-solving capabilities in complex sporting actions under competitive conditions.
Thus, a basketball player who displays a fairly
modest vertical jump, but superior reaction and
decision times, may be a far more proficient competitor than a team mate who has a remarkable vertical jump but poor reaction and decision times,
or inefficient motor coordination. In other words,
isolated biomechanical tests of strength, power and
speed may suggest that a player is eminently suited
to a given sport, but in the overall context involving
vital neural and motor control processes, he or she
may be seriously deficient.
Similarly, physiological tests may also yield an
incomplete picture of sporting capabilities. For
example, muscle biopsies that reveal a high proportion of ‘fast twitch’ (FT, type IIb) fibres may indicate
that an athlete is well suited to activities which
require the exhibition of speed, strength or power,
but adverse joint leverages, inappropriate force–
time curves for given joint actions, and inefficient
motor skill may mean that the athlete is a mediocre
performer in a given activity, such as sprinting or
jumping.
Thus, in striving to apply the methods of biomechanics to sports training, relevant information
from allied disciplines will be drawn upon wherever necessary to offer a fuller, more balanced picture of each specific situation.
105
• to enable the muscles to sustain small forces for
a prolonged period; and
• to increase muscle and connective tissue
hypertrophy.
Then, in using this information to design a suitable training approach, factors such as the following
have to be examined:
• the type of strength fitness required;
• the type of muscle contraction involved (isometric, concentric, eccentric);
• the speed of movement over different phases of
movement;
• the acceleration at critical points in the movement;
• the rest intervals between repetitions, sets and
workouts;
• active vs. passive rest/recuperation intervals;
• the sequence of exercises;
• the relative strength of agonists and antagonists,
stabilizers and movers;
• the development of optimal static and dynamic
ranges of movement;
• the strength deficit of given muscle groups;
• the training history of the individual;
• the injury history of the individual; and
• the level of sports proficiency of the individual.
The last factor is of exceptional importance because the advanced athlete responds to a given
training regime very differently from a novice. For
instance, the exact sequencing of strength, strengthspeed and hypertrophy methods in a workout or
microcycle is of little consequence during the first
weeks or months of a beginner’s training, but is very
important to a more experienced athlete.
Objectives of strength and
power training
The nature of strength
The effective and safe prescription of strength and
power training begins with an understanding of
force–time and related curves concerning the patterns of force production in sport and resistance
training. On this basis we may identify several
major objectives of strength training, namely:
• to increase maximal or absolute strength;
• to increase explosive strength;
• to increase the rate of force production;
• to enable the muscles to generate large forces for
a given period;
Successful strength and power training depends
on a thorough understanding of the factors that
influence the development of strength. The next
task is to determine which of these factors can be
modified by physical training and which methods
do so most effectively and safely. Some of these
factors are structural while others are functional.
Structural factors, however, only provide the potential for producing strength, since strength is a neuromuscular phenomenon which exploits this potential
to generate motor activity.
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muscle action in sport and exercise
It is well known that strength is proportional to the
cross-sectional area of a muscle, so that larger muscles
have the potential to develop greater strength than
smaller muscles. However, the fact that Olympic
weightlifters can increase their strength from year to
year while remaining at the same body mass reveals
that strength depends on other factors as well.
The most obvious observation is that a muscle
will produce greater strength if large numbers of
its fibres contract simultaneously, an event which
depends on how efficiently the nerve fibres send
impulses to the muscle fibres. Moreover, less
strength will be developed in a movement in
which the different muscles are not coordinating
their efforts. It is also important to note research
by Vvedensky which has shown that maximum
strength is produced for an optimum, not a maximum, frequency of nerve firing (Vorobyev 1978).
Furthermore, this optimal frequency changes with
level of muscle fatigue (Kernell & Monster 1982).
Determinants of strength
In general, the production of strength depends on the
following major structural and functional factors:
• the cross-sectional area of the muscle;
• the density of muscle fibres per unit crosssectional area;
• the efficiency of mechanical leverage across the
joint;
• the number of muscle fibres contracting simultaneously;
• the rate of contraction of muscle fibres;
• the efficiency of synchronization of firing of the
muscle fibres;
• the conduction velocity in the nerve fibres;
• the degree of inhibition of muscle fibres which do
not contribute to the movement;
• the proportion of large diameter muscle fibres
that are active;
• the efficiency of cooperation between different
types of muscle fibre;
• the efficiency of the various stretch reflexes in
controlling muscle tension;
• the excitation threshold of the nerve fibres
supplying the muscles; and
• the initial length of the muscles before contraction.
With reference to the concept of synchronizing action among muscle fibres and groups, it is
important to point out that synchronization does
not appear to play a major role in increasing the
rate of strength production (Miller et al. 1981). Efficiency of sequentiality rather than simultaneity may
be more important in generating and sustaining
muscular force, especially if stored elastic energy
and reflexive activity has to be contributed at the
most opportune moments into the movement process. Certainly, more research has to be conducted
before a definite answer can be given to the question
of strength increase with increased synchronization
of motor unit discharge.
Specificity in training
Training for enhancing strength and power is not
at all straightforward in that strength training
displays definite specificity in many respects: all
forms of strength training are different and produce
significantly different effects on neuromuscular
performance.
Fitness training for a given sport is not simply a
matter of selecting a few popular exercises from a
bodybuilding magazine or prescribing heavy squats,
power cleans, leg curls, bench press, circuit training,
isokinetic leg extensions or ‘cross-training’. This
approach may produce aesthetic results for the
average non-competitive client of a health centre,
but it is of very limited value to the serious athlete.
It is not only the exercise which modifies the body,
or, more specifically, the neuromuscular system,
but the way in which the exercise is performed. In
this regard, it is vital to remember that all exercise
involves information processing in the central nervous and neuromuscular systems, so that all training should be regarded as a way in which the
body’s extremely complex computing systems are
programmed and applied in the solving of motor
tasks (among its many other roles).
For many years, there have been two opposing theories of supplementary strength training in
sport. One theory proposes that strength training
should simulate the sporting movements as closely
as possible with regard to movement pattern, velocity, force–time curve, type of muscle contraction
strength and power training
and so forth, whereas the other maintains that it
is sufficient to train the relevant muscles with no
regard to specificity. Separate practice of technical
skills would then permit one to utilize in sporting
movements the strength gained in non-specific
training. While both approaches to strength training will improve performance, current scientific
research strongly supports the superiority of the
specificity principle in the following respects:
• type of muscle contraction;
• movement pattern;
• region of movement;
• velocity of movement;
• force of contraction;
• muscle fibre recruitment;
• metabolism;
• biochemical adaptation;
• flexibility; and
• fatigue.
In the context of training, specificity should not
be confused with simulation. Specificity training
means exercising to improve in a highly specific
way the expression of all the above factors in a given
sport. While simulation of a sporting movement
with small added resistance over the full range of
movement or with larger resistance over a restricted
part of the movement range may be appropriate at
certain stages of training, simulation of any movement with significant resistance is inadvisable since
it can confuse the neuromuscular programmes which
determine the specificity of the above factors.
Even if one is careful to apply simulation training
by using implements or loads that are similar to
those encountered in the sport, there will usually be
changes in the centre of gravity, moments of inertia,
centre of rotation, centre of percussion and mechanical stiffness of the system which alter the neuromuscular skills required in the sport.
Fundamental concepts
The development of strength and power would
appear to be a fairly straightforward quest. Since the
human constitutes an adaptive and self-regulating
organism, the imposition of progressively increasing loads on the musculoskeletal system according
to the well-known principle of gradual overload
107
would be all that is required to achieve this aim. In
this context, the load exerts a force on the body,
which uses muscle action to stabilize or move that
load, thereby giving rise to what we call strength.
Once this concept of strength/force has been introduced, we can immediately draw from mechanics a
number of other physical definitions which enable
us to formulate a scientific framework for analysing
sporting action.
Thus, strength may be defined as the ability of the
body to produce force; energy may be understood as
that physical quality which imbues an object with
the ability to exert a force; work may be regarded as
the energy involved in moving from one state or
position to another; and power refers to the rate at
which work is done at any instant.
Because force involves the movement of a limb
about a joint or fulcrum, the concept of torque (the
turning capability of a force) is frequently used in
sport biomechanics. Torque is defined as product of
a force with the perpendicular distance from the line
of action of the force to the fulcrum about which it
acts (Fig. 6.1). Sometimes, since it is defined in the
same way, torque is regarded as synonymous with
the moment of a force, and in the context of this chapter either term may be used without contradiction.
Even in the most basic applications of resistance
training, the concept of torque (or moment) is of
great practical value. For instance, the simple act of
flexing the elbows will decrease the torque acting
about the shoulder during dumbbell side raises,
supine dumbbell flyes and bench press by bringing
the load closer to the shoulder fulcrum, thereby
enhancing the safety of these exercises. Similarly,
keeping the line of action of the bar as close as possible to the body during the weightlifting clean
or powerlifting deadlift reduces the torque acting
Torque = F×d
Force
F
d
O
Fig. 6.1 Torque of a force acting at a distance d about a
fulcrum or joint centre O.
108
muscle action in sport and exercise
about the lower lumbar vertebrae and the hips,
thereby enabling a greater load to be lifted with a
greater degree of safety. The common error of swinging the bar away from the body during the later
stages of the pull during the Olympic snatch or
moving the javelin further away from the shoulder
during the wind-up for the throw are examples of
the inefficient use of torque.
The obvious implication of an understanding of
torque in the case of all joints of the body is that the
expression of strength and power is not merely a
function of changes in soft tissue structure or neuromuscular efficiency, but also of the optimal use of
torque for any sporting movement.
For instance, although the presence of a high percentage of fast-twitch muscle fibres in an athlete
may suggest that the latter may be well suited to
sports which require production of power and
speed, the existence of any inherently disadvantageous limb leverages or techniques which do not
optimize torque production in specific complex
joint actions may decree that any muscle fibre
advantage is of little consequence. Occasionally,
however, a disproportionate increase in strength
for a given activity may tend to offset these negative factors and enable the athlete to perform very
competently, albeit in a less efficient or economic
manner.
Later, the issue of torque for activities involving
several joints will be examined to caution us against
the casual analysis of joint action according to the
standard methods of functional anatomy. Hence,
we are not necessarily justified in assuming that a
given muscle produces the same joint action in a
multijoint task because the anatomy charts show
that it produces a certain joint action (such as
flexion) when only that joint is involved in the
movement. Moreover, in multijoint (multiarticular)
tasks, a muscle may exert a profound effect over
a joint which is not crossed by that muscle.
Contrary to how strength is commonly defined,
strength is not the maximal force (or torque) which
a muscle can generate; that is actually maximal
strength. To be consistent with the definition of force
according to Newton’s Laws (see later), strength is
simply the ability to generate force to overcome
inertia or a load. Similarly, we can define concepts
such as maximal torque and maximal power, as well
as optimal torque and power.
Optimization of force, torque, speed and power
or the production of ‘just the right amount at the
right time’ of these motor abilities sometimes seems
to be forgotten, especially in the so-called strength,
heavy or contact sports. All too often, the solution to
most performance problems in such sports seems to
be a philosophy of ‘the greater the strength and the
greater the muscle hypertrophy, the better’, despite
the fact that one constantly witnesses exceptional
performances being achieved in these sports by
lighter and less strong individuals.
This identifies a fundamental factor in training
for strength and power, namely the importance
of developing optimal hypertrophy, strength and
power to suit a given individual in a given activity,
and avoiding the tendency to develop superfluous
hypertrophy or redundant general strength. To
identify such inappropriate conditioning, it is
helpful to calculate relative strength (one’s maximal
load divided by body mass, in any given lift) and
to see how this changes in relation to sportspecific changes in one’s chosen sport. If performance remains much the same, while one’s relative
strength remains the same or decreases along with
an increase in overall body mass or lean body mass,
then this indicates that the increase in hypertrophy
is redundant. If relative strength and maximum
strength both increase, but performance remains
static, then this suggests that technical skills and
psychological factors (such as motivation) need to
be carefully scrutinized.
Since bodily motion is the result of muscle action
and its underlying metabolic processes, one needs
to distinguish between internal and external energy
and work. Externally, assuming no losses by heat or
sound, mechanical energy generally occurs in the
form of potential energy (PE) and kinetic energy
(KE), where PE is the energy possessed by a body by
virtue of its position and KE is the energy which a
body has by virtue of its velocity.
Although external work is defined popularly as
the product of the force and the distance through
which it is exerted, this definition applies only if the
force is constant and acts strictly along the path joining the starting and end points of the movement.
strength and power training
End
point
B
Force
Starting
point
A
Work
Displacement
Fig. 6.2 Graphic definition of work as the area under the
force–displacement curve.
The mathematical definition based on integral calculus generally is avoided in training texts, because
it is felt that it may not be adequately understood
by the practitioner, while the popular definition
usually attracts the condemnation of the scientist,
because of its limited applicability and scope. For
this reason, a definition of work in terms of energy
changes is given, namely:
work (W) = final energy – initial energy
= final (PE + KE) – initial (PE + KE)
Alternatively, we could draw a graph of how the
force varies with displacement; then work would be
given by the area under the curve between the starting and end points of the action (Fig. 6.2).
Since some of the fundamental equations used
to analyse sporting movements may be expressed
in the form of suitable graphs, this same graphic
approach may be adopted to enable us to visualize
more simply the implications of biomechanics for
training and competition.
In this respect, the following relationships will be
seen later to play an especially important role in the
biomechanics of strength and power in sport:
• force vs. time (or torque vs. time);
• force vs. displacement (and torque vs. joint angle);
• force vs. velocity; and
• rate of force development vs. time.
Initial implications of
Laws of Mechanics
Because of their fundamental importance, Newton’s
three Laws of Motion warrant repetition here:
109
• Newton I (Law of Inertia): a body will persist in
its original state of rest or motion unless acted on by
an external agent (i.e. a force).
• Newton II (Law of Acceleration): Newton stated
it as ‘The change of motion is proportional to the
motive force impressed; and is made in the direction
of the straight line in which that force is impressed’
(Richards et al. 1962). In modern terms it may be
restated as: the rate of change of velocity (acceleration) is proportional to the resultant force acting on
the body and is in the same direction as the force, or,
if suitable units are chosen, force = mass × acceleration (F = m × a).
• Newton III (Law of Reaction): for every action
there is an equal and opposite reaction.
Despite the familiarity of these laws, some of their
implications appear to be forgotten in the practical
setting, in particular regarding comparison between
machine and free weight training. Some machine
manufacturers advertise that their variable resistance machines are superior to free weights, because,
in the latter case, the weight remains constant and
does not change in response to altering joint leverages throughout range of any movement. Newton’s
first two laws show clearly that this claim is false,
since a load may only be lifted if its weight (due to
gravitational acceleration) is overcome by the lifter
with an acceleration which exceeds that of gravity.
Furthermore, during the lift, proprioceptive feedback makes the athlete aware that the load is changing and enables him to intervene voluntarily in the
loading process by accelerating or decelerating the
bar to increase or decrease the force involved. This
method is sometimes known as compensatory acceleration training (CAT) and can be useful in altering
muscle tension or movement velocity to achieve a
specific training goal.
Although the role of CAT is well known during
concentric movement (in which the load is being
overcome), its vital role during eccentric movement
(in which the load overcomes the propulsive force)
is inadequately appreciated. In non-ballistic eccentric motion in which muscle contraction continues
throughout the movement, the muscles try to oppose
the effects of the gravity to slow down and ultimately halt the downward motion of the bar. In ballistic motion, in which muscle action is intermittent,
110
muscle action in sport and exercise
so-called antagonistic muscle action comes into play
to slow down and halt the limb to ensure that the
joint is not dislocated or soft tissues are ruptured.
Even during isometric action (in which no external limb movement is apparent), compensatory processes are at play if no movement is to occur, since
neural activation changes due to fatigue, altered
mental focus or other physiological processes. This
means that the athlete has to maintain adequate
muscle tension for the entire duration of the isometric action, either by means of involuntary conditioned reflex action or by voluntary intervention.
The implication for the well-known ‘principle of
progressive overload’ is that ‘overload’ should refer
not simply to the use of progressively greater resistance over a given period, but also to the progressive
increase in muscle tension, which may be produced
by involuntary or voluntary processes. This change in
tension may be produced in ways which relate directly
to Newton II and which pose a question of fundamental importance to all strength training. It is relevant to examine this issue before we go any further.
Since force F = m × a, we may apply it to produce
the same magnitude of force F in several different
ways.
1 F = M × a, where the mass M is large and the
acceleration is small.
2 F = m × A, where the mass is small and the acceleration A is large.
3 F = m × a, where both mass and acceleration are
moderate.
This might immediately suggest, since the production of an adequate level of muscle tension is
necessary for strength training, that all of these
methods of ‘force training’ are entirely the same and
it is just a matter of personal choice which method is
used. So, the question is: does it make any real difference which method of strength training is used,
as long as adequate muscle tension is produced?
If one attempts to answer this question in purely
mechanistic terms, one might be tempted to reply ‘no’
and qualify one’s reply with comments about initiating movement against heavy loads with high inertia,
possible detrimental effects of sustained loads on
the soft tissues of the body, and duration of loading.
Interestingly, practical experience from three
different competitive aspects of strength training,
namely Olympic weightlifting, powerlifting and
bodybuilding, offers some preliminary information.
Option 1, with very heavy loads, is most commonly
encountered in powerlifting, whereas the hypertrophy associated with bodybuilding generally is a
product of option 3 training, with moderate loads
performed for about 8 –12 repetitions. Option 2 is
characterized by many actions in track-and-field
events. Olympic weightlifting, which involves lifting heavy loads rapidly, appears to contradict
evidence that velocity decreases with load, but this
is because weightlifting is ballistic and relies on
the quick movement of the lifter under the bar. It
may be concluded that powerlifting is essentially
strength generating, while weightlifting is maximum power generating in nature.
The practical evidence shows that the above three
ways of generating force do not produce the same
results and research reveals that this is because different neural, muscular and metabolic processes are
involved in each case. Thus, strength and power training are not simply a matter of using some generalized form of resistance training to produce adequate
physical loading and muscle tension; the principle
of specificity of training is central to the entire issue.
Some coaches maintain that maximal muscle
hypertrophy depends on tension time, with continuous tension times of 30 – 60 s per set of any exercise
being commonly recommended. The observation
that the extended use of isometric exercises of this
magnitude of duration does not produce the degree
of hypertrophy associated with dynamic exercise
(which includes eccentric action) militates against
this simplistic hypothesis. The fact that tension
fluctuates from low to high values throughout a
movement also militates against this idea. Clearly,
both hypertrophy and strength increase depend on
the existence of some minimum level of tension, but
nobody has identified what this tension threshold
should be in the case of hypertrophy. Moreover, it
is well known that novices to resistance training
respond to much lower intensities of loading both
in terms of hypertrophy and strength gains. It is
also known that the development of strength and
hypertrophy do not necessitate the induction of
fatigue during strength training, but that exercise
to momentary failure and at higher percentages
strength and power training
of one’s 1RM (one repetition maximum) are more
relevant in this respect.
Research has shown that the threshold training
stimulus necessary for increasing muscular strength
in the average person should not be less than onethird of the maximal strength (Hettinger & Muller
1953). As strength increases, the intensity of the stimulus required to produce a training effect should
be increased, and reach 80–95% of the athlete’s
maximum. It may be appropriate that the strength
of the training stimulus sometimes equals or even
exceeds the level of the competition stimulus of the
given exercise (Verkhoshansky 1977).
Thus, the development of strength requires that
the stimulus intensity be gradually increased. It was
discovered that every stimulus has a changing strengthening threshold, the achievement of which fails to
elicit any further increase in muscular strength
(Hettinger 1961). The less trained the muscles, the
further the strengthening threshold from the beginning state. The rate at which strength increases from
the initial level to the strengthening threshold,
expressed as a percentage of the current maximum
strength, is independent of sex, age, muscle group
and the level of the strengthening threshold. After the
strengthening threshold has been reached, strength
can be increased only by intensifying the training.
In this regard, according to Korobkov, Gerasimov
and Vasiliev (Verkhoshansky 1977), strength increases relatively uniformly during the initial stages
of training, independent of how the load is applied
in training, whether large or small. Approximately
equivalent increases in strength are obtained with
loads of 20, 40, 60 and 80% of 1RM. An increase
in the intensity of training in the initial stages (e.g.
using a heavier load, faster tempo of movement
and shorter intervals between sessions) does not
always enhance the effectiveness of strength development, this becoming effective only later, as
strength increases. This principle is corroborated by
the training results of weightlifters (Hettinger 1961;
Verkhoshansky 1977).
Specific definitions of strength
Now that some of the fundamental biomechanical
aspects of strength and power have been discussed,
111
we can return to examine the phenomenon of
strength more closely.
At the outset, it is vital to remember that strength
is the product of muscular action initiated and
orchestrated by electrical processes in the nervous
system of the body. We have seen that strength is
the ability of a given muscle or group of muscles to
generate muscular force under specific conditions,
while maximal strength is the ability of a particular
group of muscles to produce a maximal voluntary contraction in response to optimal motivation
against an external load. This strength is usually
produced in competition and may also be referred
to as the competitive maximum strength, CFmax. It is
not the same as absolute strength, which usually
refers to the greatest force that can be produced
involuntarily by a given muscle group by, for
example, electrical stimulation of the muscles or
recruitment of a powerful stretch reflex by impulsive heavy loading. It should be noted, however, that
absolute strength is sometimes used to define the
maximum strength which can be produced by an
athlete, irrespective of body mass.
It is vital to recognize a training maximum (TFmax)
or training 1RM (single repetition maximum),
which is always less than the competition maximum, CFmax, in experienced athletes, because
optimal motivation invariably occurs under competitive conditions (Fig. 6.3). Zatsiorsky states that
the training maximum is the heaviest load that one
can lift without substantial emotional excitement, as
Absolute strength
Strength deficit
Competitive maximum
Training maximum
Fig. 6.3 Different types of maximal strength. Absolute
strength is produced under involuntary conditions,
whereas the other two maxima are the result of voluntary
action. The strength deficit is the percentage difference
between absolute and maximal strength.
112
muscle action in sport and exercise
indicated by significant rise in heart rate before the
lift (Medvedev 1986). It is noteworthy that, in the
untrained person, involuntary or hypnotic conditions can increase strength output by up to 35%,
but by less than 10% in the trained athlete. The mean
difference between TFmax and CFmax is approximately 12.5% in experienced weightlifters, with a
larger difference being exhibited by lifters in heavier
weight classes (Zatsiorsky 1995).
The merit of identifying the different types of
strength or performance maxima lies in enabling
one to prescribe training intensity more efficiently.
Intensity is usually defined as a certain percentage
of one’s maximum, and it is most practical to choose
this on the basis of the competitive maximum,
which remains approximately constant for a fairly
prolonged period. The training maximum can vary
daily, so, while it may be of value in prescribing
training for less qualified athletes, it is of limited
value for elite competitors. It is relevant to note that
competitions involve very few attempts to reach a
maximum, yet they are far more exhausting than
strenuous workouts with many repetitions, since
they involve extremely high levels of psychological
and nervous stress. The high levels of nervous and
emotional stress incurred by attempting a competitive maximum require many days or even weeks to
reach full recovery, even though physical recovery
would appear to be complete, so this type of loading
is not recommended as a regular form of training.
In other words, any attempt to exceed limit
weights requires an increase in nervous excitation
and interferes with the athlete’s ability to adapt,
if this type of training is used frequently. In
attempting to understand the intensity of loading
prescribed by the apparently extreme Bulgarian
coaches who are reputed to stipulate frequent use of
maximum loads in training, one has to appreciate
that training with a training maximum (which does
not maximally stress the nervous system) is very
different from training with a competitive maximum
(which places great stress on nervous processes).
Strength is a relative phenomenon depending on
numerous factors, so it is essential that these conditions are accurately described when strength is
being assessed. For instance, muscular strength
varies with joint angle, joint orientation, speed of
movement, muscle group and type of movement,
so it is largely meaningless to speak of absolute
strength without specifying the conditions under
which it is generated. Sometimes, the term relative
strength is introduced to compare the strength of
subjects of different body mass. In this context,
relative strength is defined as the strength per unit
body mass produced by a given individual under
specific conditions (e.g. executing a well-defined
lift or combination of lifts, such as the squat, snatch
or the weightlifting total).
In determining whether an athlete requires a
specific type of resistance training, it sometimes is
useful to introduce the concept of strength deficit
(Fig. 6.3), which is defined as the percentage difference between maximum strength (voluntary effort)
produced in a given action and absolute strength
(involuntary effort) of which the athlete is capable
in that same action. This deficit may be defined
under static or dynamic conditions, with the deficit
depending on the rate at which force has to be
developed in a given joint action. In the laboratory
situation, absolute strength may be estimated by
subjecting the muscles concerned to the maximum
electrical stimulation which can be tolerated.
Strength deficit reflects the percentage of maximal strength potential which is not used during a
given motor task, but its accurate measurement is
seldom performed in practice, because determination of maximum eccentric strength by electrical
stimulation is a difficult and potentially harmful
task, and even if this were not the case, most sporting actions involve many muscles and joints, so
that measurements of deficits for separate muscle
groups would not necessarily relate to performance
deficits in complex tasks.
The closest one can approach involuntary recruitment of as many muscle fibres in a given task is to
force the body to react by reflex action to a suddenly
imposed load. Thus, in a jumping or pulling activity, an approximate measure of strength deficit may
be made by comparing the vertical jump achieved
from a static start with knees flexed with a vertical
jump preceded by a sudden dip. If there is a small
difference between the two jumps, this suggests
that training focuses more on nervous stimulation
via the use of ‘shock’ and ballistic methods such
strength and power training
as plyometrics (stretch-shortening rebound type
training). If the deficit is large, then strength and
hypertrophy training with 5RM to 8RM loads using
methods such as CAT (compensatory acceleration
training) is more suitable, with a definite emphasis
on the eccentric deceleration phase.
In general, if the strength deficit is large for a
given muscle group, an increase in speed-strength
may be produced by maximal or near-maximal
neuromuscular stimulation (e.g. via weightlifting or
plyometric methods). If the strength deficit is small,
hypertrophy must be induced by submaximal loading methods as commonly used in bodybuilding,
followed by maximal efforts against heavy loads.
Verkhoshansky (1977) has shown that the strength
deficit increases as the external resistance and the
time of motion decrease, indicating that training to
increase maximal strength becomes more important as the time available for a movement becomes
longer. Conversely, training to increase rapidity of
movement (i.e. nervous system conditioning) becomes more important as the external load decreases.
This implies that identification of explosive strength
deficit is especially important in devising strength
training regimes for athletes whose movements
allow them little time to produce maximum force, in
other words, for actions such as running, jumping,
weightlifting and throwing.
Before concerning oneself about strength deficit,
it is important to appreciate that superior performance does not depend simply on the ability to produce
maximum force, since many sporting actions take
place so rapidly that it is impossible to recruit an
adequate number of muscle fibres. Presuming that
technical skill is adequate, performance may also be
limited by the inability to produce the optimal level
of strength at any given instant or in a crucial phase
of movement (known as the accentuated region of
force production). In other words, rate of force development (RFD) is another factor vital to sporting prowess.
Thus, it is highly relevant to estimate deficits in
maximal force production, as well as in the RFD.
Identification of a strength deficit for the most
important muscle groups of an athlete enables the
coach to design the specific type of strength training
more accurately than relying on the more conventional approach of somewhat arbitrarily prescribing
113
a certain number of sets and repetitions of several
exercises with a given load. Development of the
necessary type of sport-specific fitness entails far
more than this: the training programme must also
pay careful attention to many other factors including the method of executing each exercise and the
manner in which force is displayed relative to time
and space.
A more enduring type of strength fitness results
from a well-sequenced combination of functional
and structural resistance training. However, it is
important to monitor regularly any change in relative strength to ascertain if increased hypertrophy
is simply adding unproductive tissue bulk without
a commensurate increase in functional strength.
Other useful measures of training effectiveness are
the analysis of injury or soreness patterns, and
changes in flexibility, motor skills and reaction time.
Muscle action
All sporting movement is the consequence of
muscle action, so an understanding of the different types of muscle action is another basic component of biomechanics.
Traditionally, the following types of muscle
contraction are defined: isotonic (constant muscle
tension), isometric (constant muscle length), isokinetic (constant velocity of motion) and isoinertial
(constant load). In addition, movement may occur
under concentric (muscle shortening) and eccentric
(muscle lengthening) conditions. Before these terms
are unquestioningly applied to exercise, it is important to examine their validity.
Isometric literally means ‘same length’, a state
which occurs only in a relaxed muscle. Actually, it is
not muscle length, but joint angle which remains
constant. Contraction means ‘shortening’, so that
isometric contraction, like all other forms of muscle
contraction, involves internal movement processes
which shorten the muscle. Isometric contraction
may be defined more accurately to mean muscle
contraction which occurs when there is no external
movement or change in joint angle. It occurs when
the force produced by a muscle exactly balances
the resistance imposed upon it and no movement
results.
114
muscle action in sport and exercise
The term isotonic, however, should be avoided
under most circumstances, since it is very rare for
muscle tension to remain the same while joint
movement occurs over any extended range. Constancy is possible only over a small range under
very slow or quasi-isometric conditions of movement for a limited time (since tension reduces with
fatigue or other neuromuscular changes). Whenever movement occurs, muscle tension increases
or decreases, since acceleration or deceleration is
always involved and one of the stretch reflexes may
be activated. European and Russian scientists prefer
to use the term auxotonic, which refers to muscle
contraction involving changes in muscle tension
and length. Other authors use the term allodynamic,
from the Greek allos meaning ‘other’ or ‘not the
same’. Both terms are more accurate than isotonic in
this context.
Isotonic action is most likely to occur under static
conditions, in which case we have isotonic isometric
action. Even then, as is the case with all muscle activation, there is a rise time of tension build-up, an
intermediate phase of maximal tension, and a final
decay time of tension decrease. For any prolonged
action, the tension oscillates irregularly over a range
of values. If the load is near maximal, the muscles
are unable to sustain the same level of static muscle
tension for more than a few seconds and the situation rapidly becomes anisotonic isometric.
The word isokinetic is encountered in two contexts: firstly, some textbooks regard it as a specific
type of muscle contraction, and secondly, so-called
isokinetic rehabilitation and testing machines are
often used by physical therapists. The term isokinetic
contraction is inappropriately applied in most cases,
since it is impossible to produce a full-range muscle
contraction at constant velocity. To produce any
movement from rest, Newton’s first two Laws of
Motion reveal that acceleration must be involved,
so that constant velocity cannot exist in a muscle
which contracts from rest and returns to that state.
Constant velocity can occur only over a part of the
range of action.
Similarly, it is biomechanically impossible to
design a purely isokinetic machine, since the user
has to start a given limb from rest and push against
the machine until it can constrain the motion to
approximately constant angular velocity over part
of its range. The resistance offered by these devices
increases in response to increases in the force produced by the muscles, thereby limiting the velocity
of movement to roughly isokinetic conditions over
part of their range.
One of the few occasions when isokinetic action
takes place is during isometric contraction. In this
case, the velocity of limb movement is constant and
equal to zero. However, it should be pointed out
that, even if a machine manages to constrain an
external movement to take place at constant velocity, the underlying muscle contraction is not occurring at constant velocity.
Two remaining terms applied to dynamic muscle
action need elaboration. Concentric contraction
refers to muscle action which produces a force that
overcomes the load being acted upon; therefore,
Russian scientists call it overcoming contraction.
Eccentric contraction refers to muscle action in
which the muscle force yields to the imposed load.
Thus, in Russia, it is referred to as yielding contraction. As with isometric contraction, it has been suggested that unique neural commands may control
eccentric contractions, especially since the neural
drive to the muscles is reduced, despite maximal voluntary effort under high-tension loading
(Westing et al. 1988; Westing et al. 1991; Enoka 1996).
Since superimposed electrical stimulation was
found to increase eccentric torque by more than
20% above voluntary levels and electrically evoked
torque alone exceeded voluntary torque by about
12%, it is obvious that the maximum eccentric
torque obtained voluntarily does not represent the
maximal torque-producing capacity (Westing et al.
1990). Interestingly, no corresponding differences
were observed between superimposed and voluntary torques under isometric or concentric conditions, so that neural mechanisms may protect
against the extreme muscle tension that could
otherwise develop under truly maximal eccentric
conditions. Comparison between EMG recordings
during eccentric and concentric exercise, as well as
the magnitude of the training-induced changes in
the EMG, also suggest that muscular activity under
eccentric loads may be impaired by mental processes (Handel et al. 1997).
strength and power training
A little appreciated fact concerning eccentric
muscle contraction is that the muscle tension over
any full-range movement is lower during the eccentric phase than the isometric or concentric phases,
yet eccentric activity is generally identified as being
the major cause of delayed-onset muscle soreness
(DOMS). Certainly, muscle tension of 30– 45%
greater than concentric or isometric contraction can
be produced by near-maximal eccentric muscle contraction, as when an athlete lowers a supramaximal
load in a squat or bench press (but can never raise
the same load), but this degree of tension is not
produced during the average submaximal training conditions. Interestingly, it has been shown
that muscle adaptation to eccentric loading can
be achieved by a single session of between 10 and
50 repetitions of submaximal eccentrics, and that
increased numbers of repetitions do not increase the
protective effect on muscle (Brown et al. 1997).
Eccentric training may have special value in
enhancing adaptation to strength training, as is suggested by research which revealed that submaximal
eccentric exercise encourages faster initial adaptation to strength training than similar training with
near maximal concentric loading (Hortobágyi et al.
1996). Moreover, greatest concentric muscle EMG
and tension has been observed at higher joint velocities, whereas eccentric activity increases as joint
velocity decreases (Potvin 1997).
Isometric training
In athletics, isometric exercises were very popular in
the mid-1950s as a result of the search for effective methods of developing strength. Hettinger and
Muller established that one daily effort of twothirds of one’s maximum exerted for 6 s at a time for
10 weeks will increase strength about 5% per week
in the average person (Hettinger 1961), while Clark
and colleagues found that static strength continues
to increase even after the conclusion of a 4-week
programme of isometric training (Verkhoshansky
1977).
The success of isometric training provoked considerable research, much of it being concerned with
the question of its effectiveness compared with
dynamic training. This research produced rather
115
contradictory data but showed that isometric training can be more effective than dynamic exercises in
cases where the specific exercise requires muscle
contraction of large magnitude at a certain stage of
a movement or during the early stages of injury
rehabilitation.
If the sport involves high-speed movement,
then sustained isometric training is less effective.
Research indicates that there are distinct differences
between the training effects of static and dynamic
exercises. It is important that muscular tension
should be increased slowly and be held for a relatively long time when executing isometric exercises, if the purpose is to develop absolute strength.
Prolonged maintenance of muscular tension
requires an energy expenditure that stimulates
adequate adaptation in the neuromuscular system,
thereby determining its strength potential. The
increase in strength can be more significant than
that produced by transient dynamic tension.
A technique known as oscillatory isometrics may
also be useful in producing powerful contractions
over a small range of movement. This is corroborated by research which showed that the maximum
tension that can be produced voluntarily during
sinusoidally pulsed brief isometric jerks at 5 Hz
is the same as the maximum sustained tension
(Soechting & Roberts 1975). Basmajian (1978) commented that this emphasizes the importance of
muscle fibre recruitment in the gradation of tension
and synchronization of motor unit activity during
the short bursts of loading.
In other applications, short periods of lowfrequency mechanical vibration (10 –35 Hz) on the
body have been shown to induce faster recovery,
have a positive effect on different body systems,
modulate muscle activity, elicit a higher stable state
of strength and power, lower arterial pressure,
and enhance oxidative processes (Kopysov 1978;
Lebedev & Peliakov 1991). More recently, it has
been found that powerful whole-body vibrations
imposed at 26 Hz through the lower extremities
produce marked increases in jumping power (Bosco
et al. 1998).
These findings may relate to a similar impulsive
loading process which is associated with the training effects of plyometrics, thereby adding further
116
muscle action in sport and exercise
Slow isometrics
Isometric contraction
Voluntary isometrics
Voluntary explosive
isometrics
Reflexive explosive
isometrics
Reflexive isometrics
Oscillatory isometrics
fuel to the debate (van Ingen Schenau et al. 1997)
about which of the following effects may predominate during plyometrics: elastic energy storage/
utilization in the soft tissues, neural facilitation or
intrinsic muscle changes.
At this point it must be stressed that isometric
training is not simply a matter of holding a static
muscle contraction for a given time. Isometric contraction requires a muscle to increase its tension
from rest to a maximum or submaximal value over a
certain time (the ‘rise time’), to sustain this tension
for another period (the resistance time) and to
decrease this tension to rest or a lower value (the
‘decay time’). Consequently, one may distinguish
between explosive isometrics, which have a very brief
Absolute strength
160
Force (kgf)
120
Fisometric
80%
60%
80
40%
20%
40
0
0.2
0.4
0.6
0.8
Time (s)
Fig. 6.5 The force–time graph of explosive-isometric
tension Fisometric and dynamic work with 20, 40, 60 and
80% of maximum strength for a leg-press movement.
(From Verkhoshansky 1977.)
Fig. 6.4 Categorization of the
different types of isometric muscle
action.
rise time, and slow isometrics, with a much longer
rise time. The isometric contraction may be produced by voluntary contraction or involuntarily by
the reflex response of the muscle between the eccentric and concentric phases of plyometric activities
such as the depth jump or weightlifting clean-andjerk. The different types of isometric contraction are
categorized in Fig. 6.4.
Each class of isometric training produces its own
distinct training effects. If isometric exercises are
executed with the accent on the speed of developing
force, then they can be as effective for developing
explosive strength as dynamic exercises. The steepness of the force–time curve (Fig. 6.5) and the
greater magnitude of maximum isometric than
dynamic maximum force for equivalent joint angles
is the basis for this assertion. In general, the harder
the muscles work in overcoming large resistance,
the more closely the work becomes isometric, as
may be seen from the force–velocity curves of
muscle action (see Figs 6.8 & 6.10). In other words,
isometric work is really the limiting case of dynamic work as the velocity of movement tends to
zero. Furthermore, because the inhibitory effects
usually associated with voluntary muscle action are
not encountered in reflexive isometric contraction,
even greater explosive force can be displayed isometrically than dynamically.
In connection with this, it makes sense to distinguish between isometric training for developing
absolute strength and isometric training for developing explosive strength, and to use each of
them in the appropriate situation. However, this
strength and power training
still requires detailed experimental corroboration.
Nevertheless, isometrics should not be neglected as
a means of strength and power development.
If the purpose is to develop explosive strength, then
the isometric tension should be generated with the
maximum speed possible. The reflexive explosive
isometric action produced by plyometric movements can be extremely effective in this respect.
Isometric training is reputed to produce maximum
strength gains at or very close to the angle at which
the isometric exercise is used, so that athletes often
avoid this form of training. This observation of specificity must be viewed more critically, since other
studies have shown that isometric training also produces strength increases over a range of up to 15° on
either side of the training angle (Thepaut-Mathieu
et al. 1988). This work revealed that this regional
specificity of isometric training tends to be exhibited
most strongly when the muscle is most shortened
and least when the muscle is most lengthened.
In other words, isometric training of muscles in a
relatively lengthened state can produce substantial
strength increase not only near the region of training, but also throughout the range of movement.
This finding, however, should not be interpreted to
mean that isometric training can replace other forms
of strength training, because the production of a
specific type of static or dynamic strength depends
on neuromuscular factors which govern the pattern
and manner in which muscular force is to be exerted
in a given situation.
The difference between static and dynamic
muscle contraction lies not in the muscle, but in the
nervous system, which controls the intensity, speed,
duration, type and pattern of contraction. It is the
nervous system which recruits a specific group and
number of muscle fibres at a particular rate, time
and sequence. It activates prime movers, antagonists, assistant movers, emergency muscles and
other groups of muscles to produce the necessary
controlled movement of a given joint or series of
joints. What needs to be appreciated is that the scope
of isometrics is broader than is intimated by most
texts on training.
Maintenance of a maximal isometric contraction, however, depends ultimately on autonomic
responses produced by muscle fatigue or reflexes
117
elicited in the muscles or connective tissues. Motivation may overcome the negative feedback from
these tissues for somewhat longer, but voluntary
activation of the muscles eventually becomes impossible and rest becomes necessary.
Isometric contractions may be submaximal or
maximal, of short or long duration (depending
on the length and frequency of rest intervals), continuous or intermittent, sequenced over a series of
different joint angles, alternated between agonist
and antagonist, and alternated between different
intensities. One can voluntarily oscillate isometric
contractions between high and low levels of intensity, thereby prolonging the period of application.
Isometrics performed very slowly over a given range
of joint action are referred to below as quasi-isometrics.
One criticism of traditional training is that it often
is believed that muscle action is most efficient if
initiated from a completely relaxed state. The justification is that initial tension hinders subsequent
action and produces a slower or less-controlled
movement. However, isometric contraction released
explosively can decrease the reaction response time
by as much as 7%, particularly if associated with a
strong prestretch. When a movement is produced
from a state of complete relaxation, the subsequent
action is usually slower and less forceful (Verkhoshansky 1977).
An appreciation of its value and breadth of application should restore isometrics to a place of importance in all training. Since one of the basic principles
of PNF (proprioceptive neuromuscular facilitation)
is that mobility, or dynamic contraction, is more
primitive than stability or isometric contraction,
then stability is at a higher level of muscular learning (Knott & Voss 1977). Correct understanding
and the use of the isometric state needs to become
a vital tool in the repertoire of the scientific coach.
Quasi-isometric contraction
Since any resistance training with heavy loads constrains the athlete to move very slowly, it is relevant
to define this type of slow, dynamic isometric action
as quasi-isometric. Recognition of this discrete type
of activity is necessary, because cyclic and acyclic
force–velocity curves at near-maximal loads deviate
118
muscle action in sport and exercise
significantly from the hyperbolic relationship displayed at higher velocities (see Fig. 6.10). Unlike isometric activity, which occurs at a fixed joint angle,
quasi-isometric activity may be executed over much
of the full range of movement. Therefore, its training effects, unlike those of true isometrics, are
not produced predominantly close to a specific
joint angle. This quasi-isometric activity is highly
relevant to training for maximal strength, muscle
hypertrophy and active flexibility, rather than maximal power or speed.
One does not necessarily have to try to produce
quasi-isometric activity; it is a natural consequence
of all training against near-maximal resistance and
it takes place with most bodybuilding and powerlifting exercises, provided the lifter avoids any tendency to involve the use of momentum or elastic
rebound.
A careful distinction has to be made between the
characteristics of the machine or device against
which the athlete is working, the external actions
produced by muscle contraction and the internal
muscular processes. A device may well be designed
to constrain its torque or the force in its cables to
remain constant over most of its range, but this does
not mean that the force or torque produced about a
joint by a given muscle group remains the same
when working against this machine.
In this respect, it is essential to distinguish clearly
between force and torque, since a muscle may produce constant torque about a joint over a certain
range, but the force or muscle tension causing the
action may vary considerably. Conversely, relatively constant muscle force or tension may produce
significantly changing torque. So, if either the force
or the lever length change, there will be a change of
torque.
The polyphasic nature of muscle action
Dynamic movement is regarded as the result of a
concentric contraction, in which muscle action
overcomes the load, and an eccentric contraction,
in which muscle action is overcome by the load.
Consequently, dynamic muscle action has sometimes been described as biphasic, a term which
obscures the fact that all dynamic action involves a
static transition phase both at the start and the end
of every movement. One cannot initiate, terminate,
then repeat any movement without isometric contraction of the muscles involved.
Thus, all dynamic muscle action is polyphasic.
The initiating phase from a state of rest is always
isometric. This will be followed by either a concentric or eccentric phase, depending on the specific
movement. When this phase is completed, the joint
will come to rest for a certain period of isometric
activity, after which it will be followed by an eccentric or concentric phase to return the joint to its
original position.
Clearly, the existence of at least one isometric
phase during all joint movement must be recognized in analysing movement and prescribing exercise. Isometric contraction is not simply a separate
type of muscle training which occurs only under
special circumstances, but a type of muscle action
which is involved in all dynamic movement.
Co-contraction and ballistic movement
Sport generally calls upon the muscles to produce
two kinds of action: co-contraction and ballistic
movement (Basmajian 1978). In co-contraction, agonist and antagonist muscles contract simultaneously,
with dominance of the former producing the external motion. Ballistic movement, which occurs during actions such as running, jumping and throwing,
involves bursts of muscular activity followed by
phases of relaxation during which the motion continues due to stored momentum. The term ‘ballistic’
is used, since the course of action of the limb is
determined by the initial agonist impulse, just as the
flight of a bullet is determined by the initial explosive charge in the cartridge.
Skilled, rapid ballistic and moderately fast continuous movements are preprogrammed in the
central nervous system, whereas slow, discontinuous movements are not. The ballistic action rarely
involves feedback processes during the movement.
Feedback from the muscles and joints to the central
nervous system permits the ensuing motion to be
monitored continuously and to be modified, if
necessary. The resulting movement becomes accurately executed and the relevant soft tissues are
strength and power training
Displacement d
119
Mass m
Change with time
Multiply by velocity
Velocity v = d/t
Multiply
by mass
Momentum m· v
Change with time
Acceleration a = v/t
Change with time
Multiply
by mass
Force F = m ·a
Stress
(pressure)
Over an area A
F/A
Facilitates
Energy
Fig. 6.6 Summary of the major
fundamental concepts used in
biomechanics.
protected from injury by changes in muscle tension
and by the activation of appropriate antagonists to
control and terminate the motion.
If no sensory or proprioceptive feedback is implicated, the mode of control is termed feedforward
or ‘open-loop’ control (Smith & Smith 1962; Green
1967). Here, control is preprogrammed into the
central nervous and neuromuscular systems by
the visual and auditory systems before movement
begins, so that ongoing monitoring is not involved.
The first sign of impending programmed action is
the inhibition of antagonist contraction preceding
agonist action. Premature activation of the antagonists may not only diminish skill, but it can cause
muscle injury. During ballistic and other rapid
movement, antagonist contraction is appropriate
only to terminate motion of the limb concerned.
Not only is there no continuous antagonist activity throughout ballistic movements, but it is also
absent during discontinuous motion (Brooks 1983).
The advantage offered by feedforward processes
is speed of action, whereas its main disadvantage
is the lack of flexibility which can be offered by
feedback. Nevertheless, the importance of feedforward processes in human movement should not
be underestimated, as revealed by the value of
using regimes of visualization and autogenic training in sports preparation.
During ballistic movement, the transition isometric phase between the concentric and eccentric
phases is very brief, whereas it may be much
Work F·d
Change with time
Power W/t ( = F·v)
Torque
(moment)
F×d
longer during slower maximal efforts produced,
for instance, by a powerlifter performing the squat
or bench press. The brief isometric contraction
between the eccentric and concentric phases of a
plyometric movement is of particular importance in
speed-strength training. This is one of the ways of
producing explosive isometrics, as distinct from
slow isometrics. It is associated with the generation
of great muscular power during movements such as
the weightlifting jerk, shotput or high jump, which
combine a maximal voluntary concentric thrust of
the knee extensors, in particular, with the reflexive
contribution of explosive isometrics produced by
the knee dip.
The interrelation between all of the mechanical
concepts which have been considered so far may
be summarized conveniently in the form of a flow
diagram for ease of reference (Fig. 6.6).
The mechanics of movement
The main mechanical concepts introduced above
may now be used to analyse sporting movements in
more detail. One of the best known relationships
concerning muscle action is the hyperbolic curve
(Fig. 6.7), which describes the dependence of force
on velocity of movement (Hill 1953). Although this
relationship originally was derived for isolated
muscle, it has been confirmed for actual sporting
movement, though the interaction between several
muscle groups in complex actions changes some
Force
muscle action in sport and exercise
Force
120
After
After
(a)
Velocity
(b)
Velocity
Fig. 6.7 The relationship between force and velocity, based on the work of Hill (1953). (a) The solid curve shows the
change produced by heavy strength training. (b) The solid curve shows the change produced by low-load, high-velocity
training. (Adapted from Zatsiorsky 1995.)
aspects of the curve (Zatsiorsky & Matveev 1964;
Komi 1979).
This curve implies that velocity of muscle contraction is inversely proportional to the load, that a
large force cannot be exerted in very rapid movements (as in powerlifting), that the greatest velocities are attained under conditions of low loading,
and that the intermediate values of force and velocity depend on the maximal isometric force. The
influence of maximal isometric strength on dynamic
force and velocity is greater in heavily resisted,
slow movements, although there is no correlation
between maximal velocity and maximal strength
(Zatsiorsky 1995). The ability to generate maximum
strength and the ability to produce high speeds are
different motor abilities, so that it is inappropriate
to assume that development of great strength will
necessarily enhance sporting speed.
The effect of heavy strength training has been
shown to shift the curve upwards, particularly in
beginners (Perrine & Edgerton 1978; Caiozzo et al.
1981; Lamb 1984) and light, high-velocity training
to shift the maximum of the velocity curve to the
right (Zatsiorsky 1995). Since, in both cases, power =
force × velocity, the area under the curve represents power, so that this change in curve profile with
strength increase means that power is increased at
all points on the curve. The term ‘strength-speed’ is
often used as a synonym for power capability in
sport, with some authorities preferring to distinguish between strength-speed (the quality being
enhanced in Fig. 6.7a) and speed-strength (the quality
being enhanced in Fig. 6.7b).
The graph depicting concentric and eccentric
muscle action looks like that depicted in Fig. 6.8.
Consequently, muscular power is determined by
the product of these changes (P = FV) and reaches
a maximum at approximately one-third of the
maximal velocity and one-half of the maximal
force (Zatsiorsky 1995). In other words, maximal
dynamic muscular power is displayed when the
external resistance requires 50% of the maximal
force which the muscles are capable of producing.
The pattern of power production in sporting
activities can differ significantly from that in the laboratory, just as instantaneous power differs from
average power over a given range of movement. For
example, maximum power in the powerlifting squat
is produced with a load of about two-thirds of maximum (Fig. 6.9). Power drops to 52% of maximum for
a squat with maximal load and the time taken to
execute the lift increases by 282%. Power output and
speed of execution depend on the load; therefore,
selection of the appropriate load is vital for developing the required motor quality (e.g. maximal
strength, speed-strength or strength-endurance).
strength and power training
121
Force
Eccentric contraction
Fig. 6.8 Schematic (not to scale) of
the idealized force–velocity curves
for concentric and eccentric muscle
contraction. The change in muscular
power with speed of contraction is
also depicted. Note that power is
absorbed at negative velocities, i.e.
under eccentric conditions.
Isometric contraction
1
600
200
400
In general, therefore, the picture which emerges
from the equation of muscle dynamics is that of an
inverse interplay between the magnitude of the
load and the speed of movement, except under isometric and quasi-isometric conditions. Although
this interplay is not important for the development
of absolute strength, it is important for the problem
of speed-strength.
The above studies of the relationship between
strength and speed were performed in singlejointed exercises or on isolated muscles in vitro
under conditions which generally excluded the
effects of inertia or gravity on the limb involved.
Muscle tension or force
2
Time (s)
Power (W)
Time
1000
200
Load (kg)
Velocity
Maximum
power
1400
0
Power
0
It is interesting to note that the form of Hill’s relationship (Fig. 6.7) has been modified by more recent
research by Perrine and Edgerton (1978), who discovered that, for in vivo muscle contraction, the
force–velocity curve is not simply hyperbolic (curve
2 in Fig. 6.10). Instead of progressing rapidly
towards an asymptote for low velocities, the force
displays a more parabolic shape in this region and
reaches a peak for low velocities before dropping
to a lower value for isometric contraction (V = 0). In
other words, maximum force or torque is not displayed under isometric conditions, but at a certain
low velocity. For higher velocities (torque greater
than about 200° · s–1), Hill’s hyperbolic relation still
applies.
Power
Concentric contraction
1
2
0
Fig. 6.9 The relationship between power, load and
movement time for the powerlifting squat for a group of
top + 125 kg lifters whose mean best squat is 407 kg. If a
vertical line is drawn at a given load, the intersection with
the curves gives the corresponding power and time taken
to complete the lift. For example, the line passing through
the maximum power of 1451 W occurs for a load of 280 kg
moved over a period of 0.85 s.
0
Velocity
Fig. 6.10 Force–velocity relationship of isolated muscle
(curve 1) and in vivo human muscles (curve 2) as
determined in two separate experiments under similar
loading conditions. The hyperbolic curve (1) is based on
the work of Hill, while the other curve is obtained from
research by Perrine and Edgerton (1978).
muscle action in sport and exercise
Force
122
I
III
II
0
Velocity
Fig. 6.11 Force–velocity relationship for cyclic activity
(based on data of Kusnetsov & Fiskalov 1985).
Average force
Long jump
High jump
Squat
jump
Depth jump
Dip jump
Running
Knee angular velocity
Fig. 6.12 Force–velocity curve for different types of jump.
In the squat jump, the contractile component of the muscle
is primarily responsible for force production, whereas
elastic energy, reflexive processes and other muscle
changes play additional roles in dip (countermovement)
jumps and depth jumping. The calculated values of F and
V for high jump, long jump and sprints are also shown.
(Adapted from Bosco 1982.)
Moreover, research has shown that the velocity–
time and velocity–strength relations of elementary
motor tasks do not correlate with similar relations
for complex, multijointed movements. In addition,
other studies reveal that there is a poor transfer
of speed-strength abilities developed with singlejointed exercises to multijointed activities carried
out under natural conditions involving the forces of
gravity and inertia acting on body and apparatus.
Consequently, Kusnetsov and Fiskalov (1985) studied
athletes running or walking at different speeds on a
treadmill and exerting force against tensiometers.
Their results revealed a force–velocity (F–V) graph
(Fig. 6.11) which is very different from the hyperbolic graph obtained by Hill.
This figure also shows that jumping with a preliminary dip (or countermovement) causes the F–V
curve to shift upwards away from the more conventional hyperbola-like F–V curve recorded isokinetically or with squat jumps. For depth jumps,
the resulting graph displays a completely different
trend, where the force is no longer inversely proportional to the velocity of movement. The coordinates
describing the more rapid actions of running, highjumping and long-jumping also fall very distant
from the traditional F–V curve (Fig. 6.12).
The reason for these discrepancies lies in the fact
that movement under isokinetic and squat jumping
conditions involves mainly the contractile component of the muscles, whereas the ballistic actions of
the other jumps studied apparently are facilitated
by the release of elastic energy stored in the SEC
and the potentiation of nervous processes during
the rapid eccentric movement immediately preceding the concentric movement in each case.
Studies of F–V curves under non-ballistic and
ballistic conditions (Bosco 1982) further reinforce
the above findings that the traditional F–V curves
(Fig. 6.7) do not even approximately describe the
F–V relationship for ballistic or plyometric action.
The non-applicability of these curves to ballistic
motion should be carefully noted, especially if testing or training with isokinetic apparatus is being
contemplated for an athlete.
Other work reveals that the jump height reached
and the force produced increases after training with
depth jumps (Bosco 1982). Whether this is the result
of positive changes in the various stretch reflexes,
inhibition of the limiting Golgi tendon reflex, the
structure of the SEC of the muscle, or all of these
processes is not precisely known yet. What is obvious is that the normal protective decrease in muscle
tension by the Golgi tendon organs does not occur
to the expected extent, so it seems as if plyometric
action may raise the threshold at which significant
inhibition by the Golgi apparatus takes place. This
has important implications for the concept and
practical use of plyometrics.
strength and power training
Speed-strength and strength-speed
The preceding force–velocity curves provide a useful means of distinguishing between the different
strength-related fitness qualities. It is tempting to
refer simply to speed-strength, but this disguises
the fact that certain ‘speed-strength’ sports require
a greater emphasis on speed, while others focus
more on strength. This becomes apparent from the
force–velocity curve, which enables us to identify
various strength-related fitness qualities located
between the extremes defined by V = 0 (isometric
strength) and V = very large (explosive strength).
Examination of this force–velocity curve enables
us to recognize five different strength-related qualities (as discussed earlier):
• isometric strength at zero velocity;
• quasi-isometric strength at very low velocities;
• strength-speed at low velocities;
• speed-strength at intermediate velocities; and
• explosive strength at high velocity.
The distinction between strength-speed and
speed-strength is of particular importance in devising conditioning programmes for specific sports.
The former is relevant to training where speed
development is vital, but strength is more important, whereas the latter refers to training where
speed development against resistance is vital, but
strength acquisition is somewhat less important.
In the competitive setting, speed-strength and
strength-speed sports may be divided into the
following categories:
• Cyclical, maximum-power, short-duration running, swimming and cycling.
• Maximum power output sprint activities with
jumping or negotiating obstacles (e.g. hurdles).
• Maximum power output activities against heavy
loads (e.g. weightlifting).
• Maximum power output activities involving the
throwing of implements (e.g. shotput, hammer,
javelin).
• Jumping activities.
• Jumping activities involving an implement (pole
vault).
In the language of physics, the terms speedstrength and strength-speed are synonymous with
high power (the rate of doing work). This quantity
123
is what clearly distinguishes speed-strength and
strength-speed activities from all other types of
sport: they both produce a very high power output compared with their longer-duration, lowerintensity counterparts.
Finally, in attempting to analyse speed-strength
and strength-speed activities, one must not simply
confine one’s attention to contractile muscle processes, since these types of rapid action frequently
involve some release of stored elastic energy from
non-contractile tissues after stretching by preceding
eccentric contraction. The role of the myotatic
stretch reflex and other neural processes in facilitating powerful involuntary muscle contraction
should also be taken into account. It should be noted
that the Hill and Perrine–Edgerton curves do not
apply to actions which strongly recruit the stretch
reflex or involve the release of stored elastic energy.
The interrelation between strength and
other fitness factors
Work similar to Hill’s has been carried out to
examine the relationship between strength and
endurance, and speed and endurance. It emerges
that the strength– endurance curve is hyperbolic,
but the speed– endurance curve is similar to the
Perrine–Edgerton force–velocity curve, namely
hyperbolic over most of the range, but more
parabolic for endurance where speed is high. Figure
6.13 summarizes the interrelation between strength,
speed and endurance. Using the same approach
as the above section, it enables us to distinguish
between the variety of fitness factors involved in all
motor activities. If the activities are more cyclic
in nature, then the force–velocity curve derived
by Kusnetzov and Fiskalov should be applied
(Fig. 6.11).
The classical and revised Hill curves are useful
for distinguishing between the different strengthrelated fitness qualities. It is tempting to refer simply to speed-strength, but this disguises the fact
that certain ‘speed-strength’ sports require a greater
emphasis on speed and others on strength.
If a movement is to be analysed mathematically,
then the force developed at any instant, F(t), may be
depicted graphically (Fig. 6.14). In almost all athletic
124
muscle action in sport and exercise
Strength
Maximum strength
Strength-speed
Speed-strength
Strengthendurance
Speed
Speed
Endurance
Long-duration
endurance
Medium-duration
endurance
Short-duration
endurance
Speed-endurance
movements the beginning and end of the force
curve lie on the horizontal axis, because the movement begins and ends with zero velocity. The working-effect of the effort is given by the area under the
curve F(t) over the time interval t during which
the weight W is overcome (the shaded area). An
increase in the working-effect of the movement is
achieved by increasing this area (i.e. its momentum)
and this is one of the major goals for perfecting
athletic movements. Other major goals include
increasing the maximum force, increasing the rate
of force production (the upward slope of the
graph), and producing maximum force at the
appropriate instant. When a force is applied explosively over a very brief time interval, the resulting
rapid change in momentum is known as the impulse
of the force.
Force
Momentum
Weight (W)
F(t)
Time
Fig. 6.14 Force–time curve for a load of weight W being
overcome by a force F(t).
Fig. 6.13 The interdependence of the
motor qualities of strength, speed and
endurance. The curves (not to scale)
are based on the separate data of Hill,
Perrine and Edgerton, and Gundlach
(Siff & Verkhoshansky 1999).
As sporting performance improves, the structure
of the effort produced undergoes specific changes in
space and time which can be clearly displayed even
within relatively short periods of training, as may be
seen from the graphs describing the force profiles,
F(t) and F(s), of rapid seated knee extensions,
obtained before and after 6 months of training
(Fig. 6.15). F(t) refers to the force as a function of
time and F(s) denotes the force as a function of
displacement. The graphs reveal several features:
• there is an increase in maximum force;
• maximal force is reached more rapidly;
• maximum effort is produced closer to when
muscle tension begins;
• the movement time for the effort decreases; and
• the weight of the load is overcome more rapidly.
In exercises involving a combination of muscular
work regimes, the working force is preceded by a
phase of muscular stretching (e.g. jumping in trackand-field, figure skating and acrobatics). Thus, the
perfecting of the movement is achieved by improving the ability of the muscles to generate great force
during the transition from eccentric to concentric
work (Verkhoshansky 1977). This rapid transition
from stretching to contracting causes some decrease
in the working amplitude, i.e. there is a decrease
in the angle of the working joint during flexion
(Fig. 6.16a).
The working-effect in cyclic exercises (e.g.
running, swimming and rowing) is increased by
strength and power training
125
After
Weight
Before
Force
Force
After
Weight
Before
0
Time
0
Displacement
Fig. 6.15 The (left) force–time, F(t), and (right) force–displacement, F(s), graphs for explosive force, before and after 6
months of strength training. Weight refers to the weight of the load being overcome. (Adapted from Verkhoshansky 1977.)
improving the ability to quickly produce maximum
force from the state of deep and rapid muscular
relaxation during the passive phase of the movement. There is a simultaneous increase in the
relative duration of the relaxation phase and a
shortening of the absolute duration of the cycle
(Fig. 6.16b). Thus, during the course of enhancing
sports proficiency, the process of increasing the
working-effect of the movement is independent of
the regime, while the external work of the motor
apparatus displays a specific pattern. This pattern
is characterized principally by:
• an increase in maximum force;
• displacement of the instant of maximum force
closer to when muscle tension begins;
• an increase in the working amplitude of the
movement; and
• a decrease in the time of production of the force.
θafter
Specific forms of strength expression
Figure 6.14 shows that every sports movement displays several fundamental types of strength expression at different phases of the movement, namely
starting-strength, acceleration-strength, explosive
strength, absolute strength, and strength-endurance.
These strength types may readily be defined by
examining the characteristics of this graph and
extending its scope by drawing in some of the most
important variables, such as slope (Fig. 6.17).
Depending upon the primary coordination structure of the motor activity, muscular strength
acquires a specificity which becomes more apparent
as the athlete’s level of sports mastery grows.
Fafter
θbefore
Force
Force
Fafter
The magnitude of these changes is specific to the
type of sport.
Fbefore
Fbefore
(a)
Time
(b)
Time
Fig. 6.16 (a) Change in force, F, and joint angle, θ, for reactive-ballistic movements before and after training. (b) Change in
force of cyclical movements before and after training. (Adapted from Verkhoshansky 1977.)
muscle action in sport and exercise
Force
RFD
126
Maximum RFD = IES
Fmax
Load
moving
Weight
A
B
0.5 Fmax
Load
static
tmax
0
(a)
t0.5
Isometric
phase
tmax
0
Time
Dynamic phase
Time
Dynamic phase
(b)
Fig. 6.17 (a) Force–time curve illustrating a method for determining explosive, starting and acceleration strength in lifting
a weight. W is the weight being overcome by the force F(t). Movement occurs only when the force exceeds the weight W of
the object, namely over the shaded portion of the curve. (b) Rate of force development (RFD) curve obtained by plotting
the slope of the force–time graph vs. time. The maximum rate of force development represents the index of explosive
strength (IES) (Siff & Verkhoshansky, 1999).
The relative strength of an athlete (i.e. force
produced per unit body mass) has been defined
earlier. This index is sometimes used for comparing the strength of athletes of different body mass,
although it is particularly useful for assessing
changes in an individual over time. We also defined absolute strength as maximum involuntary
strength, while speed-strength (power) characterizes
the ability to quickly execute an unloaded movement or a movement against a relatively small external resistance.
Explosive strength characterizes the ability to produce maximal force in a minimal time. The index of
explosive strength (IES) often is estimated by dividing the maximum force (Fmax) by the time taken to
produce this level of force (tmax) (Fig. 6.17a), thus
(Zatsiorsky 1995):
IES = Fmax/tmax
although mathematically it is given by the maximum value of the slope of the force–time curve
(Fig. 6.17 b).
Explosive force production is also described by
another index called the reactivity coefficient (RC),
which is the explosive strength index relative to
body weight or the weight of the object being
moved:
RC = Fmax/(tmaxW) = RFDmax/W
The most accurate way of assessing force development at any instant is to plot the slope (tan θ) of the
force–time graph vs. time, or to use a computer to
display simultaneously the curves of force vs. time
and the slope of the F–t curve (i.e. the rate of force
development) vs. time. The maximum of this rate of
force development (RFD) curve gives a precise measure of explosive strength (Fig. 6.17 b). In addition it
may be noted that the smaller the value of tmax, the
more explosive the movement. Analysis of the F(t)
curve of explosive force reveals three further characteristics of the movement, namely:
• the maximum strength of the muscles involved
(Fmax);
• the starting-strength, or ability of the muscles to
develop force during the stage just before external
movement occurs (this always occurs under isometric conditions); and
• the acceleration-strength, or ability over time to
rapidly produce maximal external force while
developing muscle tension isometrically or during
the primary stages of a dynamic contraction.
The following formula is used to provide an index
of starting-strength (ISS, or the S-gradient), which
is exhibited during the contraction just preceding
movement of the load (Zatsiorsky 1995):
ISS = 0.5Fmax/t0.5
where t0.5 is the time taken to reach half Fmax.
strength and power training
The index of acceleration strength (IAS, or the Agradient), usually used to quantify the rate of force
development (RFD) during the late stages of developing muscular force, is described by the formula:
Explosive strength is most commonly displayed in
athletic movements when the contraction of the
working muscles in the fundamental phases of the
exercise is preceded by mechanical stretching. In
this instance, the switch from stretching to active
contraction uses the elastic energy of the stretch to
increase the power of the subsequent contraction.
This specific quality of muscle is called its reactive
ability.
Strength-endurance characterizes the ability to
effectively maintain muscular functioning under
work conditions of long duration. In sport this refers
to the ability to produce a certain minimum force
for a prolonged period. There are different types
of muscle functioning associated with this ability,
such as holding a given position or posture (static
strength-endurance), maintaining cyclic work of
various intensities (dynamic strength-endurance) or
repetitively executing explosive effort (explosive
strength-endurance).
Categorization of strength capabilities into four
discrete types (absolute strength, speed-strength,
explosive strength and strength-endurance), as
explained above, can be restrictive in certain ways,
because all of them are interrelated in their production and development, despite their inherent
specificity. They are rarely, if ever, displayed separately, but are the components of every movement.
Some implications of the laws of
dynamics
The force–time curve may be regarded as one of the
graphical starting points for sport biomechanics,
just as Newton’s Second Law of Motion serves as
the corresponding mathematical starting point.
Suppose that we wish to use this information to
compare the performances of two different athletes
in executing the same exercise. They have both been
instructed to perform a single maximal repetition of
this exercise as rapidly as possible and to hold the
P
F1
Force
IAS = 0.5Fmax/(tmax – t0.5)
127
Athlete A
Athlete B
F2
0
T1
T2
T3
T4
Time
Fig. 6.18 Force curves F1 and F2, produced by different
athletes in reaching and attempting to maintain their
respective maximum forces for as long as possible in a
given exercise.
load for as long as possible until fatigue forces them
to stop. Their resulting force–time curves (Fig. 6.18)
show that athlete B exerts a greater maximal force
and continues to produce force for longer than athlete A. However, at any instant T1 between 0 and
time T2, athlete A is able to exert greater force than
athlete B. If the sport concerned requires rapid RFD
(rate of force development), then athlete A will have
the advantage.
This quality is essential in any sport which
involves jumping, striking or throwing, such as
basketball, martial arts and track-and-field. In this
case, any training aimed at increasing B’s maximal
strength or bulk will be misdirected, because he
or she needs to concentrate on explosive strength
(RFD) training. If the sport requires a high maximal
force or a large amount of momentum to be exerted
irrespective of time, then athlete B will prove to be
superior. Athlete A will not improve unless training
is directed to increasing maximal strength.
The area under the curve (i.e. the momentum)
which describes athlete B’s performance is greater
than the corresponding area for athlete A, as is the
total duration of B’s curve (i.e. reflecting muscle
endurance), so that B has a distinct advantage in
any activity that requires great momentum or great
muscle endurance during a single heavy effort. This
situation occurs in events such as wrestling, powerlifting and judo.
The informative nature of this type of analysis
also reveals the limitations of using isometric or
128
muscle action in sport and exercise
isokinetic dynamometers to assess the muscular
strength and performance of any athlete. These
devices are unable to measure functional maximal
strength, RFD or explosive strength, so it is futile to
use them in an attempt to identify functional characteristics or deficiencies to give any accurate bearing
on analysing sporting preparedness or progress.
Mechanical position during movement is preserved only within a known range, since the shape
of the force–time curve is determined by the characteristics of the neuromuscular system, imparting
to it the ability to develop muscular force with the
speed necessary to produce the required motor
effect. This ability to control muscular activity and
movement in space and time is a specific property of
the neuromuscular system and requires specialized
means of training. A lack of effective neuromuscular
training leads to errors and can cost the athlete years
of hard and fruitless work.
Most subsequent training and performance errors
are caused by inappropriate neuromuscular programming. The above-mentioned motor qualities
(force and velocity generation) of the neuromuscular system at a high level of development are
inversely proportional to one another. Excessive
development of both is not required in athletics
because they are not achieved in isolation, but are
interrelated aspects of characteristics associated
with all motor activity. Depending upon the character and the objective of the movement, one of
these qualities achieves greater development but
generally displays approximately the same pattern.
Thus, speed-strength, strength-endurance and
speed-endurance are not simply derivatives of
strength, speed and endurance, but are independent
qualities, this being emphasized by the fact that an
increase in absolute strength does not necessarily
enhance any of these three qualities. They warrant
separate recognition alongside other qualities
such as absolute strength (Verkhoshansky 1977).
However, the first attempts to devise methods for
developing these newly recognized qualities reinforced the training method which emphasizes the
separate development of each relevant quality.
For instance, this method may prescribe trackand-field exercises for developing speed in weightlifters and gymnasts, weight training for the strength
training of track athletes, and prolonged running,
swimming and other cyclic exercise for developing
general endurance in all athletes. While this may
appear to be entirely logical, it is appropriate primarily for the early stages of training and it would
be inappropriate for advanced athletes to implement this unifactorial approach exclusively. On the
other hand, this does not imply that multifaceted
preparation should be the dominant training principle, because this is true only under certain circumstances and does not adequately take into account
any interaction among the factors involved. With
growth in sporting performance, multifaceted
preparation can run counter to the law of gradual
development and hinder specific adaptation.
The universal concurrent use of a variety of general training methods or apparently similar sports
over the same period to prevent stagnation can be
counterproductive and valuable only during particular transitional stages of long-term training.
Even then, it is important to combine different
training methods or sports according to the most
appropriate sequence or combination at each stage
of preparation.
It is also not advisable to select strength training
methods which simulate sport-specific movements,
thereby misapplying the principle of dynamic correspondence and neglecting the value of using a
compendium of different methods corresponding
to the most important motor characteristics of the
given sport. This not only fails to accurately develop
the necessary fitness and motor abilities, but also
can alter the neuromuscular programmes which
control the motor actions. Instead it is important to
focus on developing the specific type of fitness and
the specific motor characteristics of the sport.
Speed, speed-strength and quickness
In apparent contradiction of the above comments,
recent findings show that the judicious superimposition of training of all relevant fitness factors
(conjugate training) is sometimes more effective
(Verkhoshansky 1977), thereby stressing that the
principles of specificity and individuality should
play a central role in the design of training programmes. This can be especially important in the
strength and power training
development of qualities which relate to the
enhancement of speed.
The patterns of sporting movement reflect the
complex non-linear sum of many functions of the
body, especially the rate of initiating the movement or increasing the speed at any stage of the
movement. Regardless of whether the athlete is a
sprinter or distance runner, a boxer throwing a
punch or a thrower accelerating a projectile, sporting prowess depends upon speed of execution.
Nevertheless, this certainly does not mean that a
particular speed quality is the sole basis for their
success. In its basic forms, speed is displayed in
simple, unloaded single-joint movements and involves relatively independent factors such as reaction time, individual movement time, ability to
initiate a movement quickly and maximum frequency of movement.
However, developing speed in simple actions
does not necessarily enhance the speed of apparently related complex movements. This is emphasized by the lack of correlation between basic forms
of speed activity and the speed of movement in
cyclic sport locomotion. This is because far more
complex neurophysiological control mechanisms
and their associated metabolic processes underlie
speed in cyclic movements. For example, many
motor qualities determine sprinting ability, such
as explosive strength, acceleration ability in the
start, the development and maintenance of maximum movement speed, and resistance to fatigue
(Verkhoshansky 1977).
Speed in sport movements comes primarily from
strength and specific types of endurance, although
this does not exclude the role of quickness (the
ability to initiate movement rapidly from a static
state without prestretch), which is just as inherent
as strength and endurance, but is displayed fully
only when the external resistance of the movement does not exceed 15% of maximal strength
(Verkhoshansky 1977).
Speed of movement is associated largely with the
fast and slow fibre composition of the muscles,
which possess different contractile and metabolic
qualities (Komi 1979). It has been fairly well established that athletes who possess a large proportion
of fast fibres in their muscles, under equal condi-
129
tions, display greater movement speed and ability
to generate force (Komi 1979).
In addition, excitability of the nervous system is a
factor which governs individual speed production,
as it has been shown that people with high excitability of the nervous system are distinguished by great
speed of movement (Verkhoshansky 1977). Speed
apparently has an upper limit that is determined
largely by genetics, and lack of improvement in
sprinting is not due to the existence of some ‘speed
barrier’, but to limitations imposed by an individual’s speed potential. Moreover, all factors
determining speed of movement have not been
identified yet and further progress will undoubtedly
stem from ongoing research.
It is important to point out that maximum speed
can be produced only if the corresponding movement receives sufficient energy for its execution.
Consequently, in those sports which require the
participant to attain high speeds, oppose large resistance, and resist fatigue, it is necessary to examine
not only the development of speed, but also those
physiological mechanisms involved, such as the
contractile potential of the muscles and the underlying metabolic processes. In situations where speed
of movement does not require great strength or
endurance, it should not be impaired by training
with large volumes of redundant work, especially
when one notes the relatively low training volumes
which are used by top-level sprinters.
Relying on the above background, we may deduce
now that quickness and speed of movement are
two of the most important independent characteristics in all sport, since, even in apparently less
dynamic sports there are always certain stages
where effectiveness of speed production can spell
the difference between success and failure.
Quickness is a general quality of the central
nervous system, being displayed most powerfully
during reflexive motor reactions and production of
the simplest unloaded movements. The individual
characteristics of quickness in all of the forms in
which it is displayed are determined by genetic
factors, so that the potential for its development is
limited. However, reflexes are not immutable, as
originally was shown by Pavlov. Indeed, the ability
to condition different reflexes and enhance the
130
muscle action in sport and exercise
Stimulus
Motor
coordination
Strength
Decision
phase
No preliminary stretch
Muscle
endurance
SPEED
Quickness
Reaction
time
Latency
phase
Preliminary stretch
External
conditions
Reactive
ability
Response
Movement
efficiency of feedforward mechanisms in the brain
are integral components of motor proficiency in
sport (Siff & Verkhoshansky 1999).
Speed of movement is a function of quickness,
reactive ability, strength, endurance and skill to
effectively coordinate one’s movements in response
to the external conditions under which the motor
task is to be executed (Fig. 6.19). Compared with
quickness, there is far greater potential to enhance
speed of movement.
It is important now to recall that different actions
in sport rely on the same major motor apparatus
and processes. The body does not employ narrow,
specialized mechanisms for satisfying each motor
demand, such as the production of speed, strength
or endurance, but uses a multipurpose system
which can control a vast array of different actions.
This remarkable ability to adapt to unusual environmental conditions is the result of the functional
growth of those systems which resist extreme
stresses, such as are encountered in sport.
Thus, an increase in the athlete’s special workcapacity is associated not with the development of
each fitness quality alone but with the functional
specialization of all bodily systems in a manner
which produces a high degree of strength, speed or
endurance. This information enables one to establish more effective methods for the special physical
preparation of athletes.
Conditioning for a given sport requires the development of different types of strength and endurance, a process that begins with the neuromuscular
apparatus. It depends on functional hypertrophy
of the muscles, enhanced intramuscular and inter-
Movement
time
Fig. 6.19 Factors which determine
speed of movement. A marked
decision phase occurs only if the
action is cognitive rather than
reflexive.
muscular control, and an increase in metabolic efficiency. Enhancement of muscular potential increases
absolute strength, the power of explosive effort and
the ability to execute sustained work.
Increased strength occurs by improved functioning of the intramuscular processes via an increase in
the number of motor units involved in muscle contraction, via increased motor neurone impulse frequency and via enhanced firing synchronization.
This is associated with increased intensity of excitation of the motor neurones from the neurones and
receptors of the higher motor levels (the motor
cortex, subcortical motor centres and intermediate
neurones of the spinal cortex).
Maximum strength is increased chiefly by involving large (high-threshold) motor units in the contraction, whereas endurance work requires the
activation of small (low-threshold) units. In the
latter case it is possible to alternate the activity of
different units, which enables work-capacity to be
maintained for longer. Explosive strength is manifested by a rapid increase in muscular tension and is
determined to a major extent by the nature of the
nervous excitation of the muscles. It is chiefly the
initial impulse frequency of the motor neurones and
their degree of synchronization that produces faster
mobilization of the motor units.
As discussed earlier, the force–time curve of
explosive effort is described by qualities of the
neuromuscular apparatus such as absolute strength,
starting-strength and acceleration-strength. The
validity of isolating starting-strength and acceleration-strength has been corroborated by electromyographic research, which reveals differences in their
strength and power training
neuromotor patterns, the recruitment of motor units
and the firing frequency of the motor neurones during the production of explosive force (Verkhoshansky
1977). This confirms the hypothesis that starting
strength is to a certain extent determined by the
innate qualities of the neuromuscular apparatus,
particularly the ratio of fast- to slow-twitch fibres in
the muscles (Viitasalo & Komi 1978).
Specialization of the neuromuscular system to
develop absolute, starting and acceleration-strength
is determined chiefly by the magnitude of the external resistance overcome. Thus, as the moment
of inertia of a rotating mass increases and resists
movement, the nature of explosive strength shows
that the roles of starting-strength and speed of movement decrease, while the roles of absolute strength
and acceleration-strength increase. Thus, the greater
the external resistance, the larger the role of absolute
strength. The relationship of the latter to body dimensions and phase of training is also well known.
Plyometric training
Research in the direction discussed above led to the
development of the so-called ‘shock’ (plyometric)
method of developing explosive strength, reactive
ability and power. Essentially, it consists of stimulating the muscles by means of a sudden stretch preceding any voluntary effort. Kinetic energy and not
heavy weights should be used for this, where the
kinetic energy may be accumulated by means of the
body or loads dropping from a certain height. Depth
jumps and medicine ball rebounding are two of the
exercise regimes commonly used in plyometrics.
The increase in popularity of plyometrics in the
West deems it necessary that the concept be more
rigorously defined. Plyometrics, or the ‘shock
method’, means precisely that—a method of mechanical shock stimulation to force the muscle to produce as much tension as possible. This method is
characterized by impulsive action of minimal duration between the end of the eccentric braking phase
and initiation of the concentric acceleration phase.
If the transition or coupling phase is prolonged by
more than a fraction of a second, the action may be
considered to constitute ordinary jumping and not
classical training plyometrics.
131
The activity also is not classically plyometric if the
athlete relies upon ongoing feedback processes to
control the isometric and concentric actions instead
of upon feedforward programmes established before any movement begins. True plyometric training
usually involves ballistic rather than co-contraction
processes, a concept discussed earlier.
A clear definition of the term ‘plyometrics’ is
essential, because one must distinguish between
plyometric actions, which occur as part of many
running, jumping, hurdling, striking and other
rebounding movements in sport, and plyometric
training, which applies plyometric actions as a
distinct training modality according to a definite
methodology.
The popular adoption of the term ‘plyometrics’
in the place of the original Russian term, ‘shock
method’, has produced this confusion. Consequently, plyometric action is often referred to as
‘stretch-shortening action’ in the scientific literature.
Since the word ‘pliometrics’ (sic) originally was
coined as a replacement for the term ‘eccentric’, it
might be appropriate to rename plyometric training
as powermetric training to remove any ambiguity of
meaning (Siff 1998).
Plyometric activity is characterized by the following phases of action between initiation and termination of the sequence of events (Fig. 6.20).
1 An initial momentum phase during which the body
or part of the body is moving because of kinetic
energy (KE) it has accumulated from a preceding
action.
2 An electromechanical delay phase, which occurs
when some event, such as contact with a surface,
prevents a limb from moving further and provokes
the muscles to contract. This delay refers to the time
elapsing between the onset of the action potential in
the motor nerves and the onset of the muscle contraction. Depending on joint action, this delay varies
in magnitude from about 20 to 60 ms (Cavanagh &
Komi 1979; Norman & Komi 1979).
3 An amortization phase when the KE produces a
powerful myotatic stretch reflex which leads to
eccentric muscle contraction accompanied by explosive isometric contraction and stretching of
connective tissues of the muscle complex. The
explosive isometric phase between the end of the
132
muscle action in sport and exercise
Initial momentum
phase
Final momentum
phase
EM
delay
Amortization
phase
Rebound
phase
Eccentric
contraction
Concentric
contraction
Fig. 6.20 The different phases of
a plyometric action. EM delay =
electromechanical delay between
signal to terminate initial momentum
phase and instant when eccentric
contraction begins.
Explosive
isometrics
Coupling time
including the kinetic energy imparted by concentric
contraction, augmentation of nervous processes,
and the release of some elastic energy stored in the
connective tissues of the muscle complex.
Discussion of coupling time is important because
it has a fundamental bearing on whether or not any
action may be classified as classical plyometrics.
Earlier it was stated that classical plyometrics is
characterized by a delay of no more than a fraction
of a second between the eccentric and subsequent
concentric contractions, a statement which requires
some qualification. For instance, research by Wilson
et al. (1991) examining different delay times in
the bench press, showed that the benefits of prior
stretch may endure for as long as 4 s, at which stage
it is suggested that all stored elastic energy is lost
(see Fig. 6.21a).
100
100
80
80
60
60
% decay
% decay
eccentric action and the beginning of the concentric
action lasts for a period known as the coupling time
(Fig. 6.20), which will be discussed shortly in greater
detail.
4 A rebound phase involving the release of elastic
energy from connective tissue, together with the
involuntary concentric muscle contraction evoked
by the myotatic stretch reflex and augmented nervous processes. This phase sometimes may include
a timed contribution added by voluntary concentric
contraction. The relative contributions to the process by elastic energy and nervous processes is
currently a matter of vigorous controversy (e.g. see
van Ingen Schenau et al. 1997).
5 A final momentum phase which occurs after the
concentric contraction is complete and the body
or limb concerned continues to move by means
40
20
0
(a)
40
20
1
2
3
Delay (s)
4
0
0.1
5
(b)
0.15
0.2
0.25
Delay (s)
Fig. 6.21 (a) The effect of a time delay on the additional force produced by a preliminary stretch in a bench press (based on
the data of Wilson et al. 1991). (b) The effect of a time delay on the additional force produced by a preliminary stretch in
unloaded rapid elbow flexion (from Siff & Verkhoshansky 1999).
strength and power training
Chapman and Caldwell (1985), on the other hand,
found that the benefits of prior stretching during
forearm movement were dissipated within 0.25 s, a
figure which agrees with other analyses of explosive
rebound elbow flexion without additional loading
(Fig. 6.21b). Other work by Wilson et al. (1991) examining rebound action of the chest/arms concluded
that no benefits of prior stretching are evident after
0.37 s.
This research seems to suggest that delays of as
long as a second or two can still produce significant
augmentation of the subsequent concentric phase
for some activities, but delays as short as 0.2 s are
sufficient to dissipate the benefits of prior stretch
during other activities, probably dependent on
factors such as the mass of the limbs and the types
of muscle fibre involved. Research by Bosco et al.
(1983) offers a partial solution to this apparent contradiction. They proposed that individuals with a
high percentage of FT (fast-twitch) fibres in the leg
muscles exhibit a maximum plyometric effect when
the eccentric phase is short, movement range is
small and coupling time is brief. On the other hand,
subjects with a high percentage of ST (slow-twitch)
fibres apparently produce their best jumping performance when the eccentric phase is longer, movement range is greater and the coupling time is
longer, since the actin-myosin cross-bridging attachment time is of greater duration.
It is also tempting to attribute these major differences in coupling times to the existence of specific
maximum delays for each joint action. While this
probably is true for different simple and complex
joint actions, it is also important to note that the
human body exhibits many different reflexes, each
of which acts under different conditions and at
different rates.
In particular, there are tonic (static) and phasic
(dynamic) stretch reflexes, and very rapid receptors
such as Pacinian corpuscles in joint capsules that
detect the rates of movement and allow the nervous
system to predict where the extremities will be at
any precise moment, thereby facilitating anticipatory modifications in limb position to ensure effective control and stability (Guyton 1984). Loss of this
predictive function apparently makes it virtually
impossible to run, jump, throw or catch. Other
133
receptors such as the Ruffini endings and receptors
in the ligaments like the Golgi tendon organs are
strongly stimulated when a joint is suddenly
moved, and after a slight initial adaptation they
transmit a steady response.
In addition, weightlifters and sometimes bodybuilders use the so-called prestretch principle to
produce a more powerful concentric muscle contraction to enable them to lift heavier loads. In doing
so, they begin a movement from a starting position
which imposes an intense stretch on the relevant
muscles, hold it for a couple of seconds and then
thrust as strongly as possible from that position. It
would seem that this longer delay would implicate
the more tonic type of reflex with a characteristically
longer coupling time. The action could certainly not
be called plyometric, despite the fact that prior
stretch had contributed to the subsequent concentric action. Conversely, phasic reflex activity would
more likely be implicated in the explosive movements which typify classical plyometrics and the
type of activity depicted in Fig. 6.21.
This explanation also serves to further distinguish
between plyometric action and plyometric training,
an issue discussed earlier in this section. One cannot
simply distinguish between plyometric and nonplyometric solely on the basis of coupling times,
otherwise one would have to classify jogging or
even brisk walking as classical plyometrics, because
the time taken for the ground reaction force to reach
a maximum can be less than 0.15 s. One also has to
take the force–time pattern and the rate of force
development (RFD) into account.
Flexibility and sporting performance
The effective and safe production of appropriate
levels of strength and power depends on the range
of movement (i.e. flexibility) of every joint involved,
the magnitude of this range depending on each
specific sporting movement. Thus, the functional
production of strength in any sporting activity relies
on neuromuscular control and joint stability over a
specific range of movement. In other words, the
strength and flexibility components of overall fitness
must interact in a way which is optimal for each
movement and each sporting action. To understand
134
muscle action in sport and exercise
the training of strength and other fitness qualities which involve range of movement, such as
strength-flexibility, flexibility-speed and flexibilityendurance, it is necessary to analyse the mechanisms which underlie flexibility and stretching.
Flexibility, or range of movement (ROM), is determined by:
• the structural or architectural limitations of the
relevant joint;
• the mechanical properties of the muscles and
other soft tissues of the joint;
• neuromuscular processes that control muscle
tension and length;
• the level of non-functional muscle tension in the
same or other muscles and soft tissues; and
• the pain threshold of the individual towards the
end of the movement range.
In particular, the location of skeletal prominences,
the length of ligaments, tendons and muscles, and
the sites of attachment and insertion of muscles are
all features which affect the ROM of a joint. In this
respect two types of flexibility are identifiable:
active flexibility and passive flexibility. Active
flexibility refers to the maximum ROM that can
be produced under active muscular control for a
particular degree of freedom of any joint, whereas
passive flexibility refers to the maximum ROM that
can be produced passively by imposition of an
external force without causing joint injury.
It should also be remembered that ROM for any
given action (e.g. extension) may be influenced by
simultaneous movement in another direction (e.g.
external rotation). Movement in any given direction
is not necessarily independent of preceding or concurrent movement in other directions, so that laboratory measurements of range of movement may
not be as unequivocal as is intimated by research.
The muscular system is characterized by the integrated action and interaction of many muscles associated with each joint, so that limited flexibility in
a certain direction may not simply be due to the
musculature directly opposing movement in that
direction alone, but also to limitations imposed
by other synergistic muscles and other stabilizing
soft tissues.
Stretching and flexibility training are not necessarily synonymous. Some flexibility exercises are
not stretching exercises although they increase
ROM, because they may focus entirely on modifying neuromuscular processes, in particular the
reflexes that control the functional range of movement. On the other hand, many stretching exercises
do not pay any deliberate attention to neuromuscular processes and tend to concentrate on eliciting
structural changes in the soft tissues. Thus, static
stretches may actually change the length of the
muscle complex, but have an inadequate effect
on the dynamic range of movement required in a
given physical activity. Therefore, it is vitally important to distinguish between the different types of
stretching and flexibility exercises in order to integrate the most appropriate and effective balance of
static and dynamic means of increasing functional
ROM into an overall training programme.
For sports participants active flexibility is by far
the more important, and correlates more strongly
with sporting prowess than passive flexibility
(Iashvili 1982). However, passive flexibility provides a protective reserve if a joint is unexpectedly
stressed beyond its normal operational limits.
Iashvili (1982) also concluded that traditional static
and passive stretching exercises develop mainly
passive flexibility, whereas combined strength and
stretching exercises are considerably more effective in developing active flexibility, particularly if
strength conditioning is applied in the zone of active
muscular inadequacy.
Emphasis on flexibility may neglect the equally
important mechanical qualities of the tissues comprising the joints, in particular their stiffness and
damping ratio. In other words, it is vital that these
tissues offer each joint an effective balance between
mobility and stability under a wide range of operating conditions. For instance, a joint whose tissues
have low stiffness (or high ability to be stretched
easily), but a low damping ratio (or poor ability to
absorb tensile shocks) will be especially susceptible
to overload injuries (Siff 1986).
Limitations in functional ROM should not
automatically be attributed to joint stiffness alone,
because this can lead to an unnecessary emphasis
on stretching. Limitations to full ROM can also
be caused by various forms of spurious or excessive muscle tension such as coordination tension,
strength and power training
Muscle involvement
0.40
0.35
Time (s)
135
Relaxation
0.30
Contraction
0.25
0.20
0
1
2
3
4
5
6
Level of qualification
Fig. 6.22 Muscle contraction and relaxation times of
athletes of increasing levels of qualification, as measured
by electromyography (based on data of Matveyev 1981).
Contraction time is the time from the onset of electrical
activity in the muscle to the peak force, while relaxation
time is the time taken from the signal to disappearance of
electrical activity. Level 1 refers to the novice, level 2 is
a Class 3 athlete, level 3 is a Class 2 athlete, level 4 is a
Class 1 athlete and level 5 is a Master of Sport, according
to Russian classification.
which may accompany the appropriate muscle
tension required by the given movement. This
non-functional tension can occur in both phasic
and tonic muscles before, during and after the
movement.
The level of proficiency of the athlete has a
marked influence on the reflex ability of the muscles
to contract and relax (Fig. 6.22). Rapidity of both
contraction and relaxation increases with level of
mastery, with a decrease in relaxation time becoming especially evident. The importance of teaching
athletes to relax the muscles rapidly and efficiently
to enhance the functional range of sporting movement then becomes obvious. It is no use having
highly flexible joints with well-conditioned, supple
connective tissues and a large range of movement,
if action is limited by spurious muscle tension.
This is corroborated by the finding that talented
sprinters are characterized not so much by large
increases in strength, but by an improved ability to
relax their muscles during the appropriate phases
of movement (Verkhoshansky 1996). Flexibility
training therefore should always be combined
with neuromuscular training to produce efficient,
functional ROM.
Standard anatomical textbook approaches describing the action of certain muscle groups in controlling isolated joint actions, such as flexion, extension
and rotation, frequently are used to identify which
muscles should be trained to enhance performance
in sport. Virtually every bodybuilding and sports
training publication invokes this approach in
describing how a given exercise or machine ‘works’
a given muscle group, as do most of the clinical texts
on muscle testing and rehabilitation.
The appropriateness of this tradition, however,
has recently been questioned as a result of biomechanical analysis of multiarticular joint actions
(Zajac & Gordon 1989). The classical method of
functional anatomy defines a given muscle, for
instance, as a flexor or extensor, on the basis of
the torque that it produces around a single joint,
but the nature of the body as a linked system of
many joints means that muscles which do not span
other joints can still produce acceleration about
those joints.
The anatomical approach implies that complex
multiarticular movement is simply the linear superposition of the actions of the individual joints which
are involved in that movement. However, the
mechanical systems of the body are non-linear and
superposition does not apply, since there is no simple relationship between velocity, angle and torque
about a single joint in a complex sporting movement. Besides the fact that a single muscle group can
simultaneously perform several different stabilizing and moving actions about one joint, there is
also a fundamental difference between the dynamics of single and multiple joint movements,
namely that forces on one segment can be caused
by motion of other segments. In the case of uniarticular muscles or even biarticular muscles (like the
biceps or triceps), where only one of the joints is
constrained to move, the standard approach is
acceptable, but not if several joints are free to move
concurrently.
Because joint acceleration and individual joint
torque are linearly related, Zajac and Gordon (1989)
consider it more accurate to rephrase a statement
such as ‘muscle X flexes joint A’ as ‘muscle X acts to
136
muscle action in sport and exercise
Relative effect on knee
2
Knee accelerated
into extension
Equal knee and
ankle effects
1
Ankle accelerated
into extension
0
45
90
135
Knee angle (degrees)
accelerate joint A into flexion’. Superficially, this
may seem a matter of trivial semantics, but the fact
that muscles certainly do act to accelerate all joints
has profound implications for the analysis of movement. For instance, muscles which cross the ankle
joint can extend and flex the knee joint much more
than they do the ankle.
Biomechanical analysis reveals that multiarticular muscles may even accelerate a spanned joint in a
direction opposite to that of the joint to which it is
applying torque.
In the apparently simple action of standing, the
soleus, usually labelled as an extensor of the ankle,
accelerates the knee (which it does not span) into
extension (Fig. 6.23) twice as much as it acts to accelerate the ankle (which it spans) into extension for
positions near upright posture (Zajac & Gordon
1989). In work derived from Lombard’s Paradox
(‘antagonist muscles can act in the same contraction
mode as their agonists’), Andrews (1985, 1987)
found that the rectus femoris of the quadriceps and
all the hamstrings act in three different ways during cycling, emphasizing that biarticular muscles
are considered enigmatic. This paradox originally
became apparent when it was noticed that in actions
such as cycling and squatting, extension of the knee
and the hip occurs simultaneously, so that the
quadriceps and hamstrings are both operating concentrically at the same time. Theoretically, according to the concept of concurrent muscle antagonism,
the hamstrings should contract eccentrically while
180
Fig. 6.23 Effect of the soleus muscle
on the angular acceleration of the
knee relative to the ankle. (Adapted
from Zajac & Gordon 1989.)
the quadriceps are contracting concentrically, and
vice versa, since they are regarded as opposing
muscles.
Others have shown that a muscle which is capable
of carrying out several different joint actions does
not necessarily do so in every movement (Andrews
1982, 1985). For instance, the gluteus maximus,
which can extend and abduct the hip will not necessarily accelerate the hip simultaneously into extension and abduction, but its extensor torque may
even accelerate the hip into adduction (Mansour &
Pereira 1987).
The gastrocnemius, which is generally recognized as a flexor of the knee and an extensor of the
ankle, actually can carry out the following complex
tasks (see Fig. 6.24):
1 flex the knee and extend the ankle;
2 flex the knee and flex the ankle; and
3 extend the knee and extend the ankle.
During the standing press, which used to be part
of Olympic weightlifting, the back bending action of
the trunk is due not only to a Newton III reaction to
the overhead pressing action, but also to acceleration caused by the thrusting backwards of the triceps muscle which crosses the shoulder joint, as
well as the elbow joint. This same action of the triceps also occurs during several gymnastic moves on
the parallel, horizontal and uneven bars. This backextending action of the triceps is counteracted by
the expected trunk-flexing action of the rectus
abdominis and the hip extension action of the hip
strength and power training
137
Knee/ankle moment–arm ratio
1.0
Fig. 6.24 The three possible actions
of gastrocnemius revealed by the
relative moment-arm ratios of the
knee and ankle joints. (Adapted from
Zajac & Gordon 1989.)
Knee flexion
Ankle flexion
Knee flexion
Ankle extension
0.5
Knee extension
Ankle extension
0.0
45
flexors, accompanied by acceleration of the trunk by
the hip flexors.
Appreciation of this frequently ignored type of
action by many multiarticular muscles enables us to
select and use resistance training exercises far more
effectively to meet an athlete’s specific sporting
needs and to offer superior rehabilitation of the
injured athlete.
Finally, because of this multiplicity of actions associated with multiarticular complex movement, Zajac
and Gordon stress a point made by Basmajian (1978),
namely that it may be more useful to examine muscle
action in terms of synergism rather than agonism
and antagonism. This is especially important, since
a generalized approach to understanding human
movement on the basis of breaking down all movement into a series of single joint actions fails to take
into account that muscle action is task dependent.
Conclusions
Various biomechanical issues and factors have been
covered, and the different types of strength and
power introduced, including speed-strength, startingstrength, explosive strength and reactive ability,
and how they all relate to the implementation of a
suitable training programme for athletes at different
stages of proficiency. This discussion, however,
should not be regarded as definitive or complete,
because of the vast number of issues which concern
the wide array of modern sports. Some central issues
90
135
180
Knee angle (degrees)
have only been touched upon, such as the biomechanics of muscle action, underlying neural programming and the involvement of connective tissue. In
addition, despite much research, many questions
remain unanswered.
Besides factors such as starting-strength,
acceleration-strength, explosive strength and relative
strength, most of the other factors which concern
the conditioning of the athlete for sport-specific
strength and power may conveniently be summarized in the form of a pyramidal model (Fig. 6.25).
In implementing any of the methods suggested
by this chapter, it is most relevant to heed the words
of N.A. Bernstein about the central role played by
efficiency of movement and the situationally appropriate utilization of the forces and different structures of the body involved: ‘The movement of the
body becomes more economical and consequently
more rational, the more the body utilizes reactive
and external forces and the less it relies on recruiting
active muscles’ (Zhekov 1976).
Finally, it is also highly relevant to the application of biomechanics in sport to remember what
Roger Bannister said after becoming the first person
to run the four-minute mile: ‘Though physiology
may indicate respiratory and circulatory limits to
muscular effort, psychological and other factors
beyond the ken of physiology set the razor’s edge
of defeat or victory and determine how closely
an athlete approaches the limits of performance’
(Bannister 1956).
138
muscle action in sport and exercise
MOTOR CONTROL
Skill
Strengthskill
Skillendurance
Strength
• Static
• Dynamic
Speedskill
Strengthspeed
Strengthendurance
Speedstrength
Flexibility
Flexibilityendurance
Endurance
• Static
• Dynamic
• Static
• Dynamic
Flexibilityspeed
Speedendurance
Speed
Fig. 6.25 A pyramidal model of
some of the important elements of
musculoskeletal fitness.
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PART 2
LOCOMOTION
Chapter 7
Factors Affecting Preferred Rates of Movement
in Cyclic Activities
P.E. MARTIN, D.J. SANDERSON AND B.R. UMBERGER
Introduction
Many human movements are characterized by the
continual repetition of a fundamental pattern of
motion (e.g. walking, running, hopping, cycling,
swimming, rowing). For cyclic activities, the average speed of progression is defined by the product
of the average distance travelled per cycle of motion
(e.g. running stride length) and the average rate
or cadence at which the cycle of motion is being
repeated (e.g. running stride rate or cadence). In
normal human movements, these speed, distance
and cadence factors are usually freely determined
or self-selected by the performer and are rarely fixed
or pre-established. In addition, humans have an
incredible ability to intentionally alter speed, distance and cadence to meet the demands of the environment. As an example, Nilsson and Thorstensson
(1987) observed that over a normal range of walking
speeds (1.0–3.0 m · s–1), subjects were able to walk
with a lowest possible stride rate of 25 strides ·
min–1 at the lowest speed and a highest possible rate
of 143 strides · min–1 at all speeds. Within a range of
running speeds (1.5–8 m · s–1), subjects could run
with rates as low as 33 strides · min–1 to as high as
214 strides · min–1. Given this ability to alter cycle
cadence and distance factors, how is the preferred
cadence chosen, and how does it relate to different
optimality criteria? The mechanisms that underlie
the selection process leading to a particular cadencedistance combination chosen by a performer for
a given activity at a given speed are not clear,
although numerous factors have been considered.
While much information has been gained about
the neurophysiology of rhythmic movements,
especially in lower vertebrates and invertebrates,
relatively little attention has been directed to understanding how cycle distance and cadence are determined and controlled by the neuromusculoskeletal
system in humans. Nevertheless, it is useful to gain
some understanding of how cycle distance and
cadence are related, even though available evidence
applies primarily to walking. Laurent and Pailhous
(1986) had subjects walk overground while imposing only stride rate or stride length by means of
auditory or visual cues and allowing all other gait
parameters to vary freely. Results revealed that
when one parameter (e.g. stride rate) was steadily
increased the other parameter (i.e. stride length)
remained almost constant despite the lack of constraint imposed on all other parameters. Moreover,
Laurent and Pailhous found that stride rate and
length were each strongly correlated with speed,
but were relatively independent of each other. The
authors proposed that speed, not rate or length, is
the critical parameter around which locomotion is
organized. Indeed, Diedrich and Warren (1995)
found that subjects make the transition from a walk
to a run at a critical speed (2.2 m · s–1), rather than at
a critical stride rate or length, when rate and length
are experimentally manipulated. Even if speed is
the parameter around which locomotion is ultimately organized, the flexibility with which stride rate
and length can be altered implies that the central
nervous system (CNS) must have mechanisms for
actively controlling these variables.
143
144
locomotion
Because of the lack of dependence between stride
rate and length, it has been suggested that rate and
length are modulated by two distinct neural control
schemes, frequency modulation for rate and amplitude modulation for length (Zijlstra et al. 1995).
Bonnard and Pailhous (1993) also proposed that
stride rate and length are controlled differently by
the nervous system. Changes in stride rate are associated with changes in the global stiffness of the
lower limb during the swing phase, but not during
the stance phase, suggesting that rate is altered
by changing the tonic activity of the lower limb
muscles during swing. Changing the tonic activity
of most or all of the muscles of the limb will alter
the resonant frequency of that limb as it swings
about the hip joint. Bonnard and Pailhous further
suggested that transient changes in stride length
are linked to phasic activation of appropriate leg
muscles. Patla et al. (1989) have shown that transient increases in stride length are indeed produced
by phasic increases in the activity of some muscles,
and by decreases in the activity of others.
While stride rate and length may follow fairly
fixed patterns during unrestrained walking and
running, the CNS has the ability to dissociate rate
and length if required or desired. Hogan (1984) proposed a physiological mechanism that would allow
such a dissociation. When antagonistic muscles are
simultaneously active about a joint, the net joint
moment is related to the difference between antagonistic muscle forces and joint stiffness is associated with the sum of muscle forces. If the CNS
actively modulates the coactivation of antagonistic
muscles, stride rate and length can be varied independently within limits. As coactivation is metabolically costly, one might hypothesize that the
preferred movement patterns require the least coactivation. This leads to the possibility that cyclic
activities are organized to minimize demands placed
on the neuromusculoskeletal system (e.g. minimizing energy cost, muscle activation, or muscle stress;
or maximizing mechanical efficiency).
This review focuses specifically on the rate or
cadence at which cyclic movements are produced
and potential factors that influence preferred or
self-selected cadences. A wide variety of factors
that may be associated with or that directly affect
preferred cadence (e.g. energy cost or economy of
movement, mechanical work or power, muscular
efficiency, muscle stress, inertial characteristics
of swinging limbs, movement pattern variability,
neuromuscular fatigue, lower extremity stiffness)
have been examined over the course of many decades of research in movement science. In addition,
research has focused on an equally wide variety of
movements or activities. While the majority of studies have investigated walking, running and cycling,
there is a more limited number of investigations on
other cyclic activities such as hopping, stair climbing, rowing, swimming and wheelchair propulsion
that can offer additional insights into cadence determination. Our purpose is to broadly review the
existing research literature to consider those factors
that may play an important role in establishing
preferred cadences and to determine whether
selected factors appear to be especially important
in influencing fundamental preferred cadences of
numerous cyclic activities.
Minimization of movement energy cost
It is intuitively appealing to speculate that submaximal, steady-state cyclic movements are organized
such that body mass-specific rate of energy consumption (e.g. J · kg–1 · s–1) or aerobic demand (e.g.
ml · kg–1 · min–1) is minimized for a given task.
Applying this argument specifically to cadence,
energy cost for a given activity would be minimized
when self-selected or preferred cadences are used.
Data for both walking and running lend support
to this supposition. Numerous investigators (e.g.
Högberg 1952; Zarrugh et al. 1974; Cavanagh &
Williams 1982; Powers et al. 1982; Heinert et al.
1988; Holt et al. 1991, 1995; Hreljac & Martin 1993)
have measured energy cost as stride rate, and thus
stride length, were manipulated systematically during constant-speed treadmill walking or running.
Results have shown consistently that energy cost
reflects a U-shaped relationship with cadence such
that as cadence is manipulated both above and
below an individual’s self-selected or preferred
cadence, energy cost rises (Fig. 7.1). As an example,
a 5% increase or decrease in stride rate of walking
resulted in an 8–10% increase (1–2 ml · kg–1 · min–1)
preferred rates in cyclic activities
22
Aerobic demand (ml·kg–1 ·min–1)
20
18
16
14
12
–10%
MEC
–5%
PSR
+5%
+10%
Stride rate (∆% PSR)
Fig. 7.1 Most economical (MEC) and preferred cadences
or stride rates (PSR) are usually closely matched for
walking and running at a given speed. Energy cost or
aerobic demand tends to be minimized at preferred
cadences and increases as stride rate is either increased or
decreased from the preferred rate. (Adapted from Hreljac
& Martin 1993; Fig. 1.)
in aerobic demand (Holt et al. 1991, 1995; Hreljac
& Martin 1993). Self-selected cadence and stride
length for most individuals usually do not deviate
substantially from those that minimize energy cost
at a given speed of walking or running. Morgan
et al. (1994) found that only 20% of a pool of 45
recreational runners reflected a stride length that
deviated by more than a few centimetres (5% of
leg length) from the most economical stride length
and showed a difference in aerobic demand between preferred and most economical conditions
that was greater than 0.5 ml · kg–1 · min–1. These
results provide convincing evidence that most
individuals self-optimize walking and running
cadences, and suggest that minimizing energy cost
may be an important factor contributing to cadence
determination.
Similar responses of energy cost or aerobic
demand to cadence changes have been shown for
145
other activities as well. Seven competitive racewalkers were most economical at their preferred stride
rate/stride length combinations and displayed
progressively higher energy costs as cadence was
either increased or decreased from the preferred
rate (Morgan & Martin 1986). In addition, van der
Woude et al. (1989) studied the effect of cadences
ranging from 60 to 140% of preferred cadence on
several cardiorespiratory measures during handrim wheelchair propulsion on a motor-driven treadmill. Aerobic demand at the preferred cadence was
approximately 10% lower than that for cadences
either 60% or 140% of the preferred value. U-shaped
relationships between aerobic demand and cadence
were observed for both experienced and inexperienced wheelchair users at several speeds of
progression, although the response of the inexperienced users was less uniform and consistent
across speeds. Despite the fact that the preferred
cadence of experienced wheelchair users increased
systematically by more than 50% (from 0.67 to
1.03 Hz) as speed of progression was increased
from 0.55 to 1.39 m · s–1, the preferred cadence at
each speed remained the most economical cadence.
Considering all of the energy cost or economy
research considered thus far, preferred and most
economical cadences appear to match well for multiple forms of gait and wheelchair propulsion. A
common feature of both types of activities is the
presence of distinct propulsion and swing phases,
even though magnitudes of muscular and contact forces are substantially different for gait and
wheelchair propulsion.
Unfortunately, minimization of energy cost is not
generalizable to all cyclic activities. Cycling and arm
cranking appear to be two tasks for which preferred and most economical cadences are different.
Numerous investigators (e.g. Seabury et al. 1977;
Jordan & Merrill 1979; Hagberg et al. 1981; Böning et
al. 1984; Coast & Welch 1985; Marsh & Martin 1993,
1997) have examined the effect of pedalling cadence
on aerobic demand or energy cost under a variety
of power outputs and for subject groups differing
in terms of fitness status and experience with the
locomotion activity. In general, aerobic demand or
energy cost reflects a curvilinear relationship with
cadence such that minimum demand occurs at
146
locomotion
3.2
200W
Aerobic demand (l·min–1)
2.8
2.4
PC
MEC
2
100W
1.6
1.2
40
60
80
100
120
Cadence (r.p.m.)
Fig. 7.2 Preferred cadences (PC, shaded region) for
cycling at a given power output tend to be substantially
higher than most economical cadences (MEC), although
some investigators have shown that MEC increases as
power output increases. (Adapted from Böning et al. 1984.)
about 55 – 65 r.p.m. (Fig. 7.2). Although preferred
cadences have been reported in only a few studies
(Hagberg et al. 1981; Marsh & Martin 1993, 1997),
preferred cadences are normally much higher
than the most economical cadences. For example,
Marsh and Martin (1997) reported most economical
cadences ranging from 53 to 60 r.p.m. for each of
three subject groups (highly fit cyclists, highly fit
runners, and recreationally active non-cyclists)
tested at power outputs ranging from 75 to 250 W.
Preferred cadences were approximately 90–95
r.p.m. for the fit cyclists and fit runners and between
80 (at 75 W) and 65 r.p.m. (at 175 W) for a less-fit
group of non-cyclists. Similarly, Böning et al. (1984)
reported most economical cadences ranging from 52
to 67 r.p.m. for a group of fit, amateur road-racing
cyclists for power outputs of 50–200 W, respectively. Finally, Seabury et al. (1977) found most economical cadences of 44, 54 and 58 r.p.m. for power
outputs of 80, 163 and 196 W for two trained distance runners and one recreational cyclist. Only
two of the cycling studies cited above report most
economical cadences exceeding 70 r.p.m. Coast and
Welch (1985) found that the most economical cadence
steadily increases from approximately 50 r.p.m. at
100 W to 78 r.p.m. at 300 W for five trained cyclists,
suggesting that exercise intensity may significantly
impact the most economical cadence. Although preferred cadences were not measured, they were still
likely to be well above most economical cadences
for all but the highest power outputs. Only results
from Hagberg et al. (1981), who studied seven roadracing cyclists at power outputs of about 330 W,
have shown a match between the most economical
and preferred cadences (91 r.p.m.).
Arm cranking appears to reflect an economy
response similar to that observed for cycling,
although the phenomenon for arm cranking has
received substantially less attention. Powers et al.
(1984) tested recreational runners at three armcranking cadences (50, 70 and 90 r.p.m.) under four
power outputs (15, 30, 45 and 60 W). Aerobic
demand was lowest at 50 r.p.m. for each power
output condition and increased systematically as
cadence increased. Unfortunately, Powers et al. did
not report preferred cadences for their subjects,
but other investigators have. Pelayo et al. (1997)
reported an average preferred cadence of 91 r.p.m.
for a group of 20 sedentary subjects exercising
at 80% of their maximal arm-cranking aerobic
demand, and Weissland et al. (1997) found preferred
cadence increased from 74 to 81 r.p.m. as exercise
intensity increased from 65 to 100% of maximal
capacity. Thus, preferred cadences appear to be
comparable with, or perhaps slightly lower than,
those reported for cycling. Weissland et al. also
investigated submaximal aerobic demand under
three subject-specific cadence conditions: preferred cadence and cadences either 10% greater or
10% lower than preferred. Aerobic demand was
significantly higher (approximately 8–13%) under
the highest cadence condition relative to preferred cadences. Although aerobic demand differences
between the preferred and –10% cadence conditions
were not statistically significant, aerobic demand
tended to be lower under the preferred cadence condition. Both Weissland et al. (1997) and Pelayo et al.
(1997) observed systematic increases in heart rate
as cadence increased. Considering all three armcranking studies cited here, the evidence suggests
preferred rates in cyclic activities
that the most economical cadences for arm cranking
are lower than the preferred cadences and that the
economy response for arm cranking is similar to
that observed in cycling. Nevertheless, much more
evidence is needed before any definitive conclusions can be drawn.
Maximizing mechanical efficiency
Mechanical efficiency, which has been defined in
several ways (e.g. gross efficiency, net efficiency,
work efficiency, delta efficiency; Gaesser & Brooks
1975), has also been proposed as a key element in
the processes underlying the selection of preferred
rates of movement. Even from the early 1920s it has
been known that there is a rate of movement that is
most efficient for a given power output (e.g. Hill
1922; Dickinson 1929). An examination of the notion
of maximizing efficiency of human movement is
not independent of the principle of minimization of
the energy cost since an expression of energy cost
forms the denominator of an efficiency ratio.
More specifically, changes in gross efficiency (total
mechanical power output divided by gross rate of
energy expenditure) as cadence is manipulated
under controlled power conditions are necessarily
inversely related to changes in energy cost (e.g. as
energy cost rises, gross efficiency falls). Movement
efficiency has been investigated in numerous cyclic
tasks including running (e.g. Kaneko et al. 1987),
walking (Zarrugh et al. 1974), manual working tasks
(Corlett & Mahadeva 1970), and cycling (Coast et al.
1986).
Hill (1922), using an elbow flexion task, observed
that the efficiency of muscular contractions increased rapidly to a maximum of approximately
26% and then fell more slowly as the duration of
contractions increased. Peak efficiency occurred
for contraction durations of approximately 1 s.
Hill subsequently cited cycling as an activity consistent with this 1 s optimum contraction duration.
Benedict and Cathcart (1913) had previously reported a most efficient cadence of 70 r.p.m. for
cycling. The significance of Hill’s observation, however, is muted when one recognizes that contractions of individual muscles during pedalling rarely
last for more than half a pedal cycle. Because of the
147
shape of the observed muscle efficiency function,
Hill also noted that high rates of movement of short
duration are likely to result in a substantial loss of
efficiency, whereas movement cycles of longer duration suffer from only a small decline in efficiency.
This suggests that high cadences may have a more
deleterious effect on performance than low rates.
Cavagna and Franzetti (1986) examined the effect
of cadence on mechanical power required to sustain
constant-speed walking. They noted that maintaining walking speed with long stride lengths and a
low cadence increases the magnitude of ground
contact forces, whereas use of short stride lengths in
combination with a high cadence requires that the
limbs be accelerated more frequently. They further
suggested that an optimum condition might exist at
intermediate cadences that would reduce inefficiencies created by either extreme, and used a mechanical power assessment to test this notion. Two
components of mechanical power were quantified
as cadence was varied under controlled walking
speeds: external power required to lift and accelerate the centre of mass of the body and internal
power used to accelerate the limbs relative to the
centre of mass. As predicted, external power
declined and internal power increased as stride
rate increased (Fig. 7.3). The sum of these two
power components, which provided an expression of total mechanical power required to sustain
walking speed, exhibited a minimum at intermediate cadences of approximately 34, 43 and 52
strides · min–1 for walking speeds of 4.6, 5.5 and
6.6 km · h–1, respectively. Assuming that mechanical power is somewhat reflective of demands
placed on the musculature, overall muscular effort
would be minimized at these minima.
As will be discussed below, Hull and colleagues
(Hull & Jorge 1985; Redfield & Hull 1986a) applied
a similar concept when using a joint moment cost
function to examine the relative demands of generating pedal forces and accelerating the limbs under
different cycling cadences. Their quasi-static moment
component was a function of external forces applied
to the foot via the pedal, and is analogous to
Cavagna and Franzetti’s external power expression.
Their kinematic moment component was related
to limb accelerations, which is analogous to internal
148
locomotion
2.5
Mechanical optimum
Total
Optimal
cadence
1.5
External
Moment
Power (W·kg–1)
2.0
Total
Kinematic
1.0
0.5
Internal
0.0
30
40
Quasi-static
50
60
70
Fig. 7.3 External mechanical power (that associated with
motion of the body’s centre of gravity) decreases and
internal power (that associated with motion of body
segments relative to the centre of gravity) increases as
cadence increases. Total power, which represents the sum
of internal and external components, reflects a minimum
at intermediate stride rates. (Adapted from Cavagna &
Franzetti 1986.)
power. The relationships of these variables with
respect to cadence or stride rate are strikingly similar in shape (see Figs 7.3 & 7.4) and interpretation.
Both approaches predict an optimal rate of movement. Curiously, Cavagna and Franzetti (1986)
reported that their calculated mechanically optimal
cadence for walking was 20–30% less than selfselected cadences, while Redfield and Hull (1986a)
predicted a mechanically optimal cadence approximately 10% higher than typical preferred cycling
cadences. Thus, there appear to be other factors not
accounted for in these models that influence the
determination of self-selected cadences.
Gaesser and Brooks (1975) examined the effect of
pedalling cadence and power output on multiple
expressions of efficiency. Twelve subjects rode a
stationary ergometer at cadences of 40, 60, 80 and
100 r.p.m. at power outputs of 0, 200, 400, 600 and
800 kg m · min–1. The results demonstrated that
efficiency tended to increase as power output
increased, although the responses varied depending on the efficiency definition that was used. More
Cadence
Fig. 7.4 Simulation results from Redfield and Hull (1986a)
demonstrated that joint moment contributions associated
with acceleration of the limbs (i.e. kinematic component)
increase with cadence, and contributions associated
with pedal forces acting on the foot (i.e. quasi-static
component) decrease with cadence. The sum of these two
components (total) reflects a minimum at intermediate
cadences (approximately 90–110 r.p.m.). (Reprinted from
Redfield & Hull (1986a), pp. 317–329, with permission
from Elsevier Science.)
importantly, increases in cadence resulted in a
decrease in efficiency, regardless of the efficiency
expression. Gaesser and Brooks argued that delta
efficiency, which is defined as the ratio of a change
in power output and the associated change in
energy cost, provides the best indicator of true muscular efficiency. Results from Sidossis et al. (1992)
tend to contradict those of Gaesser and Brooks. In
an assessment of the effects of power output (50,
60, 70, 80 and 90% of maximal aerobic capacity)
and cadence (60, 80 and 100 r.p.m.) on gross and
delta efficiency, Sidossis and colleagues observed
that cadence had little effect on gross efficiency.
Delta efficiency, however, increased significantly
from 20.6 to 23.8% as cadence was increased from
60 to 100 r.p.m. Sidossis et al. speculated that the
improved delta efficiency reflects an increase in
muscular efficiency under higher cadence conditions. Citing fundamental muscle research that
demonstrates peak muscular efficiency is achieved
preferred rates in cyclic activities
when fibre shortening velocity reaches one-third
of the maximum velocity of shortening (e.g.
Koushmerik & Davies 1969), they speculated that
‘by increasing the cadence, the active muscle fibres
of the cyclists in the present experiment contracted
at velocities closer to the velocity of peak muscular
efficiency’ (p. 410).
Widrick et al. (1992) argued that accelerations of
the limbs, particularly at high cadences, contribute
significantly to the muscular effort required to
maintain a given cadence and power output.
Further, they suggested that exclusion of internal
mechanical power (that associated with limb accelerations) from a total power expression ‘may confound subsequent conclusions regarding optimal
rates of limb movement’ (p. 376). Subjects pedalled
at 40, 60, 80 and 100 r.p.m. under three external
power output conditions (49, 98 and 147 W)
established using a Monark bicycle ergometer.
Their results demonstrated that internal mechanical power increased systematically as cadence
increased for each nominal external power output
condition. Thus, total mechanical power (external
power plus internal power) also increased as
cadence increased. Using energy expenditure
estimates computed from aerobic demands for
each cycling condition and total mechanical power
results, Widrick and colleagues computed mechanical efficiency. Optimal pedalling cadences, defined
as the cadence at which mechanical efficiency
was maximized, ranged from 82 r.p.m. at 49 W to
101 r.p.m. at 147 W, values that are clearly quite
comparable with preferred cycling cadences.
As one final example of the potential relationship
between preferred and most efficient rates of movement, Corlett and Mahadeva (1970) developed an
instrument to quantify mechanical power during a
manual tyre-pumping task. Combining this assessment with measures of oxygen consumption, they
were able to quantify the energy expenditure per
stroke for different pumping rates. Interestingly, the
energy cost per stroke declined as rate of pumping
increased from slow (~10 strokes · min–1) to intermediate rates (30–40 strokes · min–1). Energy cost
per stroke did not change with further increases in
rate (up to 60 strokes · min–1). Further, preferred
rates of movement coincided with the minimum
149
stroke rate at which the energy cost per stroke
reached a plateau. Although efficiency was not
quantified in this study, this minimum stroke rate
corresponds to a rate at which efficiency would be
greatest.
From this brief review of mechanical power and
efficiency, it can be seen that preferred cadences in
several cyclic activities may correspond well with
cadences at which efficiency is maximized. Unfortunately, the existing research literature related to
human movement efficiency is difficult to interpret
because of inconsistencies in the definitions of both
mechanical power and energy expenditure expressions used in efficiency ratio calculations. Additionally, mechanical power and energy expenditure can
be difficult to quantify and/or control experimentally for many activities. In part because of these
difficulties, the number of different activities investigated in efficiency studies is limited.
Mechanical optimization of
muscular effort
One approach in the search for an explanation for
preferred rates of movement is to use optimization
or modelling strategies. These strategies use modifiable characteristics, such as cadence, and kinematic
constraints to define muscle action. Such strategies
have been used to predict optimal cycling cadence
(Redfield & Hull 1986a, 1986b; Hull & Gonzalez
1988; Hull et al. 1988; Kautz & Hull 1993). In cycling,
there is an important link between pedalling cadence
and performance. Cyclists use the gears of the bicycle
to select a particular cadence suited to the riding
demands. The traditional approach has been to collect empirical data whereby metabolic cost (e.g. aerobic demand) of riding at particular combinations
of cadence and power output have been determined
(e.g. Dickinson 1929; Garry & Wishart 1931; Gaesser
& Brooks 1975; Seabury et al. 1977; Jordan & Merrill
1979; Hagberg et al. 1981; Böning et al. 1984; Coast &
Welch 1985; Marsh & Martin 1993, 1997).
Hull and colleagues have taken a different
approach to identifying essential factors that determine optimal pedalling cadence. They argued that
physiological cost, which is of considerable importance with respect to overall performance, is directly
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locomotion
associated with muscular effort and that mechanical
markers (e.g. net joint moments) can provide a reasonable representation of lower-extremity muscular
effort (Redfield & Hull 1986a,b). In their earlier
efforts, Hull and colleagues (Hull & Jorge 1985;
Redfield & Hull 1986a) developed a five-bar linkedsegment model that could be used to simulate net
joint moment profiles under many different pedalling conditions (e.g. different cadences, power
outputs, crank-arm lengths). Inputs for their model
included scaled pedal-force profiles, measured crank
positions, lower-extremity kinematic data predicted
from crank position and anthropometric constraints,
and pedal angles derived from a sinusoidal function. In an effort to delineate muscle function more
effectively, net joint moments were subsequently
divided into a quasi-static component, which was
a function of external forces applied to the foot via
the pedal, and a kinematic moment related to limb
accelerations.
Redfield and Hull (1986a) specifically explored
the relationship between net joint moments and
pedalling cadence. Net joint moments were simulated for cadences of 63, 80 and 100 r.p.m. at a power
output of 200 W. They found that as cadence
increased, the kinematic moment increased and the
quasi-static moment decreased. The increased kinematic moment was attributed to the increased accelerations of the limbs at higher speeds, whereas the
decreased quasi-static moment was a function of
the inverse relationship between pedal force and
cadence when power output is maintained. When
these components are added, a parabolic-like curve
representing the total moment is derived (Fig. 7.4).
From these results, Redfield and Hull showed that
the total joint moment is high at relatively low
cadences (< 80 r.p.m.) because of a high quasi-static
contribution. At relatively high cadences (> 120
r.p.m.), the total moment is also high because of
high kinematic moment contributions. Thus, total
joint moment is minimized, suggesting that muscular effort is minimized, at intermediate cadences
(105 r.p.m. in their analysis for a 200 W power output). Redfield and Hull concluded that their joint
moment cost function provided a valid criterion for
assessing optimal cadence for several reasons. First,
predicted optimal cadences of the order of 90–110
r.p.m. appear to agree well with preferred cadences
of experienced cyclists, rather than with the most
economical or efficient cadences (30–60 r.p.m.)
reported in the research literature (e.g. Hill 1922;
Dickinson 1929; Garry & Wishart 1931; Gaesser &
Brooks 1975). Second, predicted optimal cadence
rises with increasing power output, and third, optimal cadence appears to be relatively insensitive
to pedalling style.
Redfield and Hull (1986b) refined and extended
their simulations of optimal cycling cadence by
applying a muscle stress-based function that
had been used previously in gait research (e.g.
Crowninshield & Brand 1981). Their muscle stressbased cost function improved prediction of both
propulsive and recovery phase pedal forces as well
as net joint moments, compared with their previous
moment-based modelling efforts. Hull et al. (1988)
subsequently used the muscle stress function to predict the optimal cadence for a 200 W power output
and found a minimum in this cost function in the
range of 95 –100 r.p.m., a value that was consistent
with their earlier work using the moment cost function (Redfield & Hull 1986a). Interestingly, the close
match between the optimal cadences predicted
from the muscle-stress and net joint moment cost
functions led Hull et al. to conclude that the
moment-based function offered the advantage of
greater ease of computation without sacrificing
accuracy in predicting optimal cadence.
A crucial feature of any simulation research is the
extent to which its results can be supported by
empirical data. A fundamental assumption made
by Hull et al. (1988) was that pedal forces scale in
inverse proportion to the scaling of crank angular
velocities as pedalling cadence changes (i.e. as crank
velocity increases, pedal forces decrease). MacLean
and Lafortune (1991a) showed that while the normal component of the pedal force scaled in proportion to crank velocity during the propulsive
phase or downstroke, the reverse was true during
the upstroke or recovery phase (i.e. as cadence
increased, the normal component increased). Further, shear forces applied to the pedals increased
during the downstroke and became smaller in the
upstroke as cadence increased. They concluded
that scaling of pedal forces in inverse proportion to
preferred rates in cyclic activities
crank velocity was not acceptable. Thus, use of this
assumption may compromise the validity of model
predictions.
In a separate presentation, MacLean and Lafortune
(1991b) compared optimal cadence determined
using five net joint moment-based cost functions
with the cadence at which group mechanical
efficiency was maximized, the latter being assumed
to reflect the optimal cadence criterion. Using a
group of 10 experienced cyclists riding at 200 W
over five cadences from 60 to 120 r.p.m. (in increments of 15 r.p.m.), they found that only one of their
five moment-based cost functions (one based solely
on the net moment about the knee) yielded an
optimal cadence matching that at which gross
mechanical efficiency was maximized (80.4 and
81.3 r.p.m., respectively). The remaining momentbased cost functions yielded optimal cadences
that were substantially higher, on average about
100 r.p.m., and much nearer to values reported by
Hull and colleagues (Redfield & Hull 1986a; Hull
et al. 1988). MacLean and Lafortune suggested that
it is not surprising that minimizing the net knee
moment will minimize physiological cost and maximize gross mechanical efficiency because of the
many muscles acting about the knee in cycling.
Other issues surrounding optimization of cycling
cadence, including seat height, foot position, etc.,
have been explored and are reviewed by Gregor et
al. (1991). There remains conjecture regarding the
relationships between muscle characteristics and
selection of optimal rate (Chapman & Sanderson
1990), and these have yet to be resolved. Currently,
there are few or no published empirical data that
substantiate the supposed relationship between
muscle moments, muscle stress and cadence selection. Clearly, this needs to be a focus of ongoing
research.
Minimization of neuromuscular fatigue
Recently, a number of investigators have explored
the role of muscle fatigue in determining the optimal cadence for cycling during both steady-state
and exhaustive exercise. Sargeant (1994) has defined
muscle fatigue as ‘the failure to generate or maintain
the required or expected force or power output,
151
resulting from muscle activity, and reversible by
rest’ (p. 116). In a series of papers, Takaishi, Moritani
and colleagues (Takaishi et al. 1994, 1996, 1998) have
estimated neuromuscular fatigue, using characteristics of the electromyograph (EMG) signal, to
help explain differences between preferred and
most energetically optimal cadences in cyclists and
non-cyclists. Takaishi et al. (1994) had eight noncyclists pedal at rates ranging from 40 to 80 r.p.m.,
at 75% of maximal aerobic power. Not surprisingly, metabolic cost was minimized at the lower
cadences, and increased significantly as cadence
approached 80 r.p.m. In contrast, the slope of the
integrated EMG curve (iEMG) over the course of an
exercise bout at a given cadence was significantly
lower for the higher cadences. Over time, an
increase in the slope of the iEMG is thought to reflect
the recruitment of additional motor units, and/or
an increase in the firing frequency of previously
recruited motor units. As such, the slope of the
iEMG is directly related to the intensity of the activity (Takaishi et al. 1994).
Takaishi et al. (1996) also found that the slope of
the iEMG was lower at higher cadences (80–90
r.p.m.) in six trained cyclists, whereas metabolic cost
was minimized at 60 –70 r.p.m. In both cases, the
cadences at which the slope of iEMG was found to
be lowest were similar to the preferred cadences of
the subjects (Takaishi et al. 1994, 1996). As the slope
of iEMG was lower at higher cadences, Takaishi et
al. (1994, 1996) concluded that the higher cadences
chosen by competitive cyclists are selected to help
minimize peripheral neuromuscular fatigue. They
further noted that the lower iEMG slopes at the
higher cadences suggests that fewer type II muscle
fibres would be needed to meet the demands of the
cycling task.
In support of this contention, Ahlquist et al. (1992)
found that glycogen depletion was much greater in
type II muscle fibres after cycling at 50 r.p.m. than
at 100 r.p.m. at a power output equivalent to 85%
of maximal aerobic power. Glycogen depletion
was not different in type I fibres between the two
cadence conditions. The lower pedal forces required
at a higher cadence for a fixed power output
(Patterson & Moreno 1990) would require lower
muscle forces, and not require the recruitment of as
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locomotion
many type II fibres (Ahlquist et al. 1992). Patterson
and Moreno (1990) noted that the resultant pedal
forces were minimized at 90 r.p.m. (at 100 W) and
100 r.p.m. (at 200 W) in a group of 11 recreational
cyclists. These values were also very close to the
preferred cadences at both power outputs. During
steady-state cycling, greater recruitment of type II
fibres at lower cadences would presumably lead to
more rapid fatigue. At higher cadences, the greater
reliance on type I fibres would help prevent the
onset of fatigue. Nevertheless, metabolic energy
cost will still be higher under high cadence conditions due to the greater number of repetitions performed per unit of time (Takaishi et al. 1994, 1996).
Takaishi et al. (1996) also noted that non-cyclists
showed large increases in the iEMG of the vasti
muscles at higher pedalling rates, whereas the
trained cyclists did not demonstrate such an
increase. The authors suggested that the lack of
increase in iEMG for trained cyclists at higher
cadences was related to pedalling skill developed
by the trained cyclists. In subsequent research,
Takaishi et al. (1998) demonstrated that while the
vasti iEMG did not increase substantially for trained
cyclists (N = 7) as cadence increased, biceps femoris
iEMG did increase dramatically. Trained noncyclists (N = 7) demonstrated a general increase in
the iEMG of the vasti muscles as cadence increased,
with no increase in biceps femoris activity. In
addition, normal pedal forces decreased for both
trained cyclists and trained non-cyclists as cadence
increased; however, the normal pedal forces were
lower for trained cyclists than trained non-cyclists at
all but the lowest cadence (45 r.p.m.). The investigators suggested that the trained cyclists had
developed a pedalling technique that involved pulling up the leg, via knee flexion, during the recovery
portion of the pedal cycle at higher cadences. The
speculated technique would allow for the lower
pedal force seen in the cyclists, and presumably
result in lower muscle stress in the vasti group, and
a lower dependence on type II muscle fibres
(Takaishi et al. 1998).
Some papers in the literature would seem to contradict the findings of the above mentioned studies.
Carnevale and Gaesser (1991) found that time to
exhaustion was greater at 60 r.p.m. than 100 r.p.m.
in a group of seven untrained subjects at multiple
power levels. Similarly, McNaughton and Thomas
(1996) reported time to exhaustion was greater at 50
r.p.m. than at 90 or 110 r.p.m. for untrained subjects.
These results are consistent with the general finding
that metabolic cost is minimized around 50– 60
r.p.m. (Seabury et al. 1977; Carnevale & Gaesser
1991; Marsh & Martin 1993, 1997; McNaughton &
Thomas 1996). While the work of Carnevale and
Gaesser, and of McNaughton and Thomas is certainly relevant, it cannot be directly compared with
the studies by Takaishi et al. (1994, 1996, 1998). The
former investigations used power outputs designed
to bring about volitional exhaustion in a 1- to 10-min
range, while Takaishi et al. (1994, 1996, 1998) used
power output levels that were designed to allow
subjects to cycle for at least 15 min without suffering undue fatigue. Carnevale and Gaesser (1991)
and McNaughton and Thomas (1996) also used
untrained subjects, while Takaishi et al. (1996, 1998)
used a combination of untrained non-cyclists,
trained non-cyclists, and trained cyclists. A final
point not directly addressed by Carnevale and
Gaesser (1991) was that while time to exhaustion
was substantially greater for 60 r.p.m. vs. 100 r.p.m.
at the lowest power output, the time to exhaustion
difference between 60 and 100 r.p.m. all but disappeared as power output was increased. With regard
to this, Hill et al. (1995) suggested that the advantage
of decreased metabolic cost at lower cadences may
be offset as power output increases, due to the
increased muscle force requirements per cycle.
While the data relating to the role of muscle
fatigue in setting preferred rate of movement during different modes of cycling are as yet equivocal,
the theoretical work of Sargeant (1994) may provide
some additional insight. In a muscle of mixed fibre
type, the optimal rate of shortening will be a compromise between the power–velocity relationships
of type I and type II fibres. During real-world
cycling, maximal power output is achieved at approximately 120 r.p.m. (Sargeant 1994). Based on the
combined power–velocity relationship of a theoretical whole muscle, and the ability of the CNS to
selectively recruit motor units, Sargeant argued that
at 80% of maximal power output, pedalling at 120
r.p.m. would result in a reserve of 20% available
preferred rates in cyclic activities
power, due to the muscle being at the shortening
velocity corresponding to the peak of the power–
velocity curve. At 60 r.p.m. there would be no
power reserve, as the muscle would be on the
ascending limb of the power–velocity curve.
Pedalling at 120 r.p.m. would also allow the smallest possible contribution from type II fibres to meet
the demands of the cycling task (assuming type I
fibres were maximally activated). Sargeant additionally contends that having the smallest theoretical contribution from type II fibres requires a
progressive increase in cadence as power output is
increased. Sargeant’s model also predicts that at
lower power outputs, the demands are best met at a
lower cadence. This would allow a greater reliance
on more economical type I fibres than at higher
cadences. While the work of Sargeant (1994) is
mostly theoretical in nature, at the very least it
suggests that the preferred or optimal rate of movement during cycling, and other cyclic activities, may
well be determined in large part by underlying
mechanical properties of the specific muscles most
involved in producing the movements. At present,
this notion has not been thoroughly investigated
experimentally.
Pendular properties of swinging limbs
Kugler and colleagues (Kugler et al. 1980; Kugler &
Turvey 1987) noted that limb motions in locomotion
are auto-oscillatory and possess mechanically conservative characteristics of a pendular-like mode of
organization; in other words, the limbs represent
complex pendulum systems. During cyclic activity
of an anatomical system (e.g. walking), a certain
amount of mechanical energy is dissipated from the
system with each cycle of motion. Thus, muscular
effort is required to sustain limb pendular-like
movements. It has been hypothesized that a resonant frequency for any complex pendulum system
can be predicted if the anthropometric and inertial
characteristics of the limbs are known. Further, it
is suggested that the resonant frequency relates
directly to the fundamental rate that minimizes the
energy cost associated with sustaining the motion.
Holt et al. (1990) proposed that walking can be modelled as a force-driven harmonic oscillator (FDHO)
153
and that the resonant frequency of the FDHO model
corresponds to the preferred rate of walking.
Results for 24 young adults supported their hypothesis that ‘the resonant frequency of a harmonic
oscillator can accurately predict that chosen by subjects when appropriate adjustments are made to
the formula based on an optimization criterion of
minimum force’ (p. 64). They concluded that the
physical attributes of the lower extremity, more
specifically its inertial characteristics, specify the
most economical stride rate. In subsequent research,
Holt et al. (1991) confirmed that preferred stride rate
was not different from that predicted from their
FDHO model. Subjects walked under eight stride rate
conditions (preferred rate, rate predicted using the
FDHO model, and rates 5, 10 and 15 strides · min–1
higher or lower than the FDHO rate) as aerobic
demand was measured. Both preferred and FDHO
predicted stride rates resulted in minimal aerobic
demand, lending additional support to the association between preferred stride rate and gait economy. Although the FDHO model has not been
applied to activities other than gait, recent research
has successfully predicted preferred stride rates for
backward walking (Schot & Decker 1998) and for 3to 12-year-old children (Jeng et al. 1997), effectively
extending the generalizability of the phenomenon.
The association between the energy cost of walking and running and the inertial characteristics of
the lower extremity has been demonstrated in several segment loading studies in which segment inertia has been modified artificially (e.g. Martin 1985;
Myers & Steudel 1985; Steudel 1990). In contrasting
proximal and distal applications of load, more distally positioned load on the segment produces a
larger increase in the moment of inertia of the leg
about the hip and a greater increase in the aerobic
demand of gait than proximal loading. Less attention has been paid to the effect of load distribution
on the temporal features of walking and running.
Consistent with the pendular phenomenon, Martin
(1985) reported a small (1.2%) but statistically
significant decrease in stride rate and increase
(2.0%) in swing time when 0.50 kg was added to
each foot during treadmill running at 3.33 m · s–1.
Recent data from our laboratory have also shown
predictable effects of shank and foot loading on
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locomotion
walking stride rate in able-bodied (Royer et al. 1997)
and unilateral below-knee amputees (Mattes et al.
2000). Thus, while the FDHO model and pendular
mechanics are theoretically sound and appear to
apply well to cyclic activities in which the extremities are being oscillated, the magnitude of the
effect on cadence is not well substantiated.
Limb stiffness
Recently, Farley, McMahon, and co-workers
(Blickhan 1989; McMahon & Cheng 1990; Farley
et al. 1991; Farley et al. 1993; Farley & Gonzalez 1996;
Ferris & Farley 1997) have used a simple springmass model of the human body to demonstrate that
limb stiffness may determine rate of movement
in bounding and running gaits. According to this
model, the human body is represented as a massless
spring (the ‘leg spring’) and a point mass. It has been
shown that the stiffness of the leg spring remains
nearly constant as running speed increases in
humans and several other animal species (Farley et
al. 1993; He et al. 1991). As running speed increases,
the leg spring is swept through a larger angle,
increasing the effective stiffness of the overall system, and causing the body to bounce off the ground
at a faster rate. During hopping, or at a constant running speed, however, the stiffness of the leg spring
appears to be modulated to produce a different
hopping rate.
Farley et al. (1991) had four subjects hop forwards
on a treadmill-mounted force platform at speeds
from 0 to 3 m · s–1, and in place on a ground-based
force platform. During both hopping conditions,
and at all but the fastest treadmill speed, the mean
preferred rate was 132 hops · min–1. The body
behaved as a simple spring-mass system at the preferred hopping rate and at all rates above preferred.
Below the preferred hopping rate, the body did not
behave as a simple spring-mass system, implying
that the storage and reutilization of elastic energy
would be compromised at low rates. At hopping
rates above preferred, the stiffness of the leg spring
was increased to allow the body still to behave as a
simple spring-mass system. As ground contact time
decreased with increasing hopping rate, Farley et al.
(1991) suggested that metabolic cost would increase
at rates above preferred, as the time to generate
muscular force would be shortened. A shortened
ground contact time has been suggested to require
the recruitment of less-economical fast-twitch
muscle fibres, and consequently increase metabolic
cost (Kram & Taylor 1990). Ferris and Farley (1997)
further showed that subjects increase hopping rate
by increasing leg-spring stiffness, regardless of surface compliance. However, leg-spring stiffness was
increased disproportionately more on compliant
surfaces than stiff surfaces, to keep the total vertical
stiffness nearly constant at a given rate.
Farley and Gonzalez (1996) had four subjects run
on a treadmill-mounted force platform at 2.5 m · s–1,
and at stride rates from 26% below to 36% above
preferred (preferred stride rate = 79.8 strides ·
min–1), to see how the behaviour of the spring-mass
model was altered to produce different stride rates.
While the stiffness of the leg spring has been found
to remain constant, and the angle through which the
leg spring is swept increases as speed increases (He
et al. 1991; Farley et al. 1993), Farley and Gonzalez
found that different stride rates at a constant speed
are produced primarily by increasing the leg-spring
stiffness. The stiffness of the leg spring was increased over twofold from the lowest stride rate to
the highest rate, while the angle swept by the leg
spring only decreased slightly at the highest rate.
In fact, when stride rate (Farley & Gonzalez 1996)
and hopping rate (Farley et al. 1991) were each
increased by 65%, leg-spring stiffness increased
by approximately the same amount (twofold),
demonstrating the similarities between these two
forms of locomotion.
Farley and Gonzalez (1996) stated that the ability
to adjust the leg-spring stiffness is likely to be an
important factor in adapting the locomotor system
to the demands of the environment. In physiological
terms, the stiffness of the leg spring can be adjusted
in at least two ways. Changing the orientation of the
limbs relative to the ground (McMahon et al. 1987),
and changing muscle activation patterns (Farley &
Gonzalez 1996) will each result in an altered legspring stiffness. In summary, Farley et al. (1991) suggested their findings help explain why metabolic
cost is minimized at the preferred rate of movement
in bounding or running gaits. Metabolic cost below
preferred rates in cyclic activities
the preferred rate will increase due to a loss of
elastic strain energy from the system. Above the
preferred rate, metabolic cost will increase due to a
shorter ground contact time. While the spring-mass
model has been valuable in distinguishing important aspects of rate selection in bounding and running gaits, it is not directly applicable to other
activities, such as walking, where kinetic energy
and gravitational potential energy are 180° out
of phase, and the body does not behave as a simple
spring-mass system. Interestingly, Bonnard and
Pailhous (1993) found that during walking, stride
rate is highly dependent on limb stiffness during the
swing phase, but independent of limb stiffness during stance. The stiffness changes noted by Farley
and co-workers (Blickhan 1989; McMahon & Cheng
1990; Farley et al. 1991; Farley et al. 1993; Farley &
Gonzalez 1996; Ferris & Farley 1997) during running and hopping relate implicitly to the stance
phase.
Minimizing movement variability
In addition to metabolic cost, mechanical minimization phenomena and limb inertial properties, movement stability or variability may be another factor
that determines the preferred or optimal rate of
movement during cyclic activities. The reader
should note that high movement stability and low
movement variability are synonymous in the present context. Much, if not all, of the literature relating to movement stability during cyclic activities
comes out of a dynamical systems approach to
movement organization. According to dynamical
systems theory, ‘behavioural patterns and their
dynamics are shown to arise in a purely selforganized fashion from cooperative coupling among
individual components’ (Kelso & Schöner 1988,
p. 27). A primary focus of this theory is the study
of stability and the loss of stability. Well-learned
or preferred movement patterns are associated with
high stability, and a loss of stability is usually
indicative of an impending change in behaviour
(such as the transition from walking to running).
There is also evidence from more traditional
motor behaviour circles that movement variability
is an important and relevant issue in control of pre-
155
ferred rate of movement. Smoll (1975), and Smoll
and Schutz (1978) found distinct individual differences in preferred cadences and movement variability in a cyclic upper-limb task. They noted that
movement variability is uncorrelated with preferred cadence, and is likely to be related to underlying biological variability. According to Smoll (1975),
movement variability is indicative of the status of an
individual performance, and is an essential component of a complete description of that performance.
Movement variability has previously been characterized as stochastic in nature (Hirokawa 1989).
Recent research by Hausdorff and colleagues
(Hausdorff et al. 1995, 1996), however, has demonstrated that variations in the stride interval during
steady-state walking exhibit long-range correlations, such that the fluctuations in stride interval at
any point in time are dependent on stride intervals at previous times. The long-term correlations
extend as far back as 1000 strides (Hausdorff et al.
1996). Interestingly, when subjects walked in time
with a metronome set at their preferred stride rate,
the long-range correlations disappeared, and the
variations in stride interval became random in
nature (Hausdorff et al. 1996). Hausdorff et al. (1995)
proposed that chaotic variability is an intrinsic
part of the normal locomotor control system. The
researchers also suggested that supraspinal centres
are responsible for the presence of the long-term
correlations. From a control perspective, systems
that possess long-range correlations are inherently
more resistant to perturbations (Hausdorff et al.
1995). Movement variability/stability is clearly a
relevant factor for cyclic movement control, and
a possible determinant of preferred rate of
movement.
One of the most complete accounts of the relationship between movement stability and preferred rate
of movement is provided by Holt et al. (1995). Their
paper is notable because they employed stability,
metabolic, mechanical and inertial measures, allowing direct comparisons not usually possible in unifocal studies. They determined three measures of
movement stability for eight subjects at their preferred speed as they walked on a treadmill at preferred stride rate, optimal stride rate predicted by a
force-driven harmonic oscillator model of the lower
locomotion
Oxygen consumption (l·min–1)
1.6
0.09
Variability
Metabolic cost
1.4
0.08
1.2
0.07
1.0
0.06
0.8
0.05
0.6
60
80
100
120
Standard deviation units
156
0.04
140
Per cent of predicted frequency
Fig. 7.5 Both aerobic demand and movement variability
reflect minima near the resonant frequency or stride
rate predicted using a force-driven harmonic oscillator
model. This predicted stride also corresponded well with
preferred cadences of subjects. (Adapted from Holt et al.
1995.)
limb, and ±15, ±25 and ±35% of predicted stride rate.
The three stability measures were the standard
deviation of the relative phase between the lower
limb joints, the standard deviation of a normalized
vector length of the phase planes for the head and
back, and the magnitude of the spectral power
near the predicted and preferred frequencies for
the head and joints. They additionally measured
metabolic cost and mechanical energy conservation
at each stride rate. Holt and colleagues found that
movement stability was generally maximized (i.e.
variability was minimized) and metabolic cost
minimized at the preferred and predicted stride
rates, which were not significantly different from
each other (Fig. 7.5). Holt et al. (1995) noted that the
metabolic cost curve was steeper at low stride rates
than at high rates, but the reverse was true for the
stability curve. The investigators suggested that
preferred stride rate may be a compromise between
metabolic cost and movement stability.
Maruyama and Nagasaki (1992) measured the
variability of many temporal aspects of the stride
(stride time, step time, stance time, swing time and
double support time) using variable error and
coefficient of variation in seven subjects during
treadmill walking at speeds ranging from 0.5 to 1.7
m · s–1, and stride rates ranging from 30 to 80 strides
· min–1. The two major findings by Maruyama and
Nagasaki (1992) were that stride variability for all
stride phases decreased as speed increased, and
variability was minimized at or near the preferred
stride rate at any given speed. In a similar study
using 22 subjects walking overground, Sekiya et al.
(1997) found that spatial variability of stride length
was minimized near the preferred stride rate and
preferred speed. At the speed most closely approximating the commonly reported energetically
optimal speed (1.38 m · s–1), temporal variability
was minimized at a stride rate of 58.2 strides · min–1
and spatial variability was minimized at a stride
rate of 60.4 strides · min–1. The preferred rates at the
same speed were 57.1 strides · min–1 (Maruyama &
Nagasaki 1992) and 54.2 strides · min–1 (Sekiya et al.
1997). Maruyama and Nagasaki (1992) and Sekiya
et al. (1997) concluded that preferred stride rate is
optimized in terms of metabolic cost and movement
stability.
Brisswalter and Mottet (1996) used variability
and metabolic cost measures in an analysis of the
walk-to-run transition in 10 subjects walking and
running on a treadmill. During the preferred transition speed trials, variability increased as walking
speed increased in the neighbourhood of the transition speed. After the transition, variability was
much lower, consistent with the findings of others
(Diedrich & Warren 1995). Brisswalter and Mottet
(1996) also expected variability to be lower for walking below the transition speed, and lower for running above the transition speed; however, this was
not the case. Variability was lower for running than
walking at all common speeds (±0.3 m · s–1 of transition speed). Therefore, below the energetically optimal transition speed, walking is more economical,
but also more variable than running. In addressing this paradox, the authors noted the difficulty
in associating gross energy cost with movement
efficiency, and suggested that metabolic cost alone
is not adequate to relate movement efficiency
and variability. Another factor not addressed by
Brisswalter and Mottet is that at the common
speeds, stride rate was higher for running than for
walking (1–16%), and variability tended to decrease
(up to a point) with increases in rate of movement
preferred rates in cyclic activities
(Smoll 1975; Smoll & Schutz 1978), perhaps making
the finding of lower variability at all running speeds
less surprising. One should keep in mind that the
paper by Brisswalter and Mottet dealt with speeds
near the preferred transition speed, and did not
include data on preferred speed or stride rate for
walking or running.
In a paper dealing with the walk-to-run transition, Diedrich and Warren (1998) presented an
account of movement stability over a range of walking and running speeds. The walking stability function had a minimum at 1.66 m · s–1 and 61.8 · strides
· min–1. The data from Diedrich and Warren compare favourably with the results from Maruyama
and Nagasaki (1992). At a speed of 1.67 m · s–1,
Maruyama and Nagasaki reported minimum
variability at 62.0 strides · min–1, and a preferred
rate of 62.4 strides · min–1. While the stability and
metabolic cost relationships were very similar in
shape, the respective minima were not coincident
(energetically optimal walking speed ~1.3 m · s–1).
Diedrich and Warren (1998) emphasized the similarities between the overall behaviour of the stability and economy functions, and suggested that any
minor differences were likely to be related to the
fact that global energy expenditure includes costs
not associated with the locomotor task. As with
research by others (Maruyama & Nagasaki 1992;
Holt et al. 1995; Sekiya et al. 1997), the findings of
Diedrich and Warren (1995, 1998) point to a strong,
if not perfect (Brisswalter & Mottet 1996), relationship between movement stability and economy.
Patla (1985) examined EMG variability at fast,
normal and slow stride rates in seven subjects walking on a treadmill at preferred speed. He used a pattern recognition technique to estimate variability.
Surprisingly, muscle activity patterns were found
to be more variable for the normal stride rate than
the slow or fast rates. The author suggested that
the attentional demand necessary to walk in a
non-preferred manner could account for the lower
variability under these conditions. The finding of
increased variability for muscle activity at the preferred rate is in direct contrast to the notion that
kinematic variability is minimized at the preferred
rate (Maruyama & Nagasaki 1992; Holt et al. 1995;
Sekiya et al. 1997).
157
All of the studies reviewed so far have dealt
exclusively with adults. A few papers in the literature have dealt with movement variability during
locomotion in children. Jeng et al. (1997) determined
interlimb and intralimb stability in 45 children aged
3 –12 years walking on a treadmill at their preferred
stride rates and ±25% of preferred stride rate. In
most cases, interlimb and intralimb stability was
maximized under preferred stride rate conditions.
The authors also noted that by age 7 years, children
exhibit a self-optimization pattern similar to adults.
Jeng et al. (1997) also observed that 5- to 6-year-olds
demonstrated an ability to modulate stride rate not
seen in 3- to 4-year-olds, but as a consequence the
gait of the 5- to 6-year-olds became more variable.
Variability subsequently decreased in the 7- to 12year-olds. The dramatic differences between the
5- to 6- and 3- to 4-year-olds are possible due to morphological changes that occur between ages 3 and 6;
however, they may also be indicative of a transition
from a rigid form of control to a more adaptive form
of control (Jeng et al. 1997). A more adaptive form of
control would by its very nature require more variability in the system. Clark and Phillips (1993) have
also suggested that infants also go through a period
of stability acquisition during the first 3 months of
independent walking. Although the picture is far
from complete, locomotion development in children may undergo at least two distinct phases of
stability acquisition. One is associated with the initial development of the walking skill, and a second
is associated with an increase in the adaptability of
stride rate to meet the demands of the environment.
The literature on movement variability at different rates of movement in cyclic activities outside the
locomotion arena is sparse. Recently, Dawson et al.
(1998) reported changes in temporal variability during rowing on an ergometer and on the water in five
competitive rowers, over a range of stroke rates
(18 –33 strokes · min–1). The authors discovered that
rowers increase stroke rate primarily by decreasing
the duration of the recovery phase, while the
duration of the stroke phase changed very little.
As stroke rate increased, variability generally
decreased for both the recovery phase and the
stroke phase. The decreases in variability were most
dramatic for the recovery phase, which exhibited
158
locomotion
considerably higher variability than the stroke
phase at the lower rates. Dawson et al. (1998) did not
determine preferred stroke rate for the rowers in
their study. They did note, however, that preferred
stroke rate is usually in the range of 30–40 strokes ·
min–1. This would suggest that movement variability is minimized at or near preferred stroke rates in
competitive rowers.
Based on the studies reviewed, movement stability would appear to be a contributing factor to the
selection of the preferred cadences during locomotion. Specifically, the results of Holt et al. (1995) indicate that stability may cooperate with metabolic cost
in setting the preferred stride rate. The findings of
Dawson et al. (1998) suggest that minimizing variability may be a factor in cadence selection for other
activities as well. Many more studies will be needed
on other cyclic activities before any far-reaching
generalizations can be made regarding the role of
movement stability/variability in rate of movement
selection.
Summary
The factors that determine the preferred and/or
optimal rate of limb movement during any cyclic
activity are clearly many. Metabolic cost, mechanical minimization phenomena, muscle mechanical
properties, limb inertial parameters, movement
stability and limb stiffness all appear to be associated with the preferred rate of movement for
one or more activities. The tasks for the future are
twofold. For the locomotion arena, well-designed
multifactorial studies are needed that will allow us
to determine which associated factors are causal,
and which are merely related effects. Additionally, many studies are needed using activities other
than walking, running and cycling, to determine
whether the conclusions reached from the locomotion-based studies have strong generalizability,
or are activity specific. Only then will the critical
factors underlying the selection of the rate of movement emerge.
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Chapter 8
The Dynamics of Running
K.R. WILLIAMS
Somewhere near a speed of 2 m · s−1 a walking person will change to a running pattern of movement,
with the lack of a period of double support and the
presence of a flight phase differentiating running
from walking. Over a range of speeds from jogging
to sprinting the basic running pattern changes in a
variety of ways, generally to optimize movement
patterns at the slower speeds typical of distance
running, and to maximize power output and speed
at sprinting speeds. The changes that occur in the
kinematics and kinetics of segmental movements
are likely to result from conscious and subconscious
efforts to minimize or maximize a variety of specific
criteria, such as metabolic energy expenditure, tissue stress, muscle power, fatigue and other factors.
For competitive athletes the ultimate goal is to
improve performance, while for many others the
primary aim is maintaining or improving their state
of health and fitness, with performance only a secondary issue.
Biomechanics provides an important adjunct to
physiology, psychology and medicine in efforts to
better understand why an individual adopts a
specific movement pattern. The dynamic characteristics of running will have an effect on metabolic
energy expenditure, the fatigue process, susceptibility to injury, and other factors important to both the
elite athlete and the weekend jogger. After a short
discussion of factors that affect biomechanical measures of running, a variety of topics will be covered
that will first present some of the basic information
used to describe the dynamics of running, and then
highlight some of what is known about the influence
mechanical factors have on performance, energy
expenditure, fatigue, footwear and injury. Information specific to sprint speeds will be discussed as
appropriate. For additional information, readers are
referred to previous reviews of running (Williams
1985a; Nigg 1986; Morgan et al. 1989; Putnam & Kozey
1989; Cavanagh 1990; Mero et al. 1992; Anderson 1996).
Factors that influence
biomechanical measures
Speed of running
Almost all measures of the mechanics of movement
in running are affected by speed (Nilsson et al. 1985;
Frederick & Hagy 1986; Mero & Komi 1986; Munro
et al. 1987), and for a valid comparison of biomechanical measures between individuals or conditions it is
usually necessary to make measurements at the same
speed of running. For example, faster sprinters spend
a shorter time in contact with the ground during the
support period primarily because they are running
faster than slower sprinters. Whether a difference in
support time might also be related to better performance, beyond the speed-related differences, can
only be ascertained by comparing different abilitylevel sprinters at the same speed. If differences
between individuals or conditions are found at different speeds, it is often not possible to distinguish
the differences due to speed and the differences due
to other factors. Similar concerns are present for distance running. As a result of the influence of running speed on biomechanical measures, almost all
comparative studies of running are carried out by
controlling or matching speed.
161
162
locomotion
Gender and anthropometric influences
A runner’s gender, size and specific anatomical
structure may also influence biomechanical variables. Lutter (1985) estimated that out of 3500
injured runners examined over a 7-year period in a
sports medicine clinic, only 10% had extremities
that would be judged to be biomechanically optimal, making it likely that body structure is partly
responsible for differences in the way individuals
run. These observations are similar to ones made
earlier by James et al. (1978) who found that only
22% of 180 subjects had a neutral rearfoot alignment
during weight bearing, with 58% pronated and 20%
supinated. Biomechanical studies need to consider
whether anthropometric factors will affect the measurements being evaluated. For example, since a
relationship has been found between the amount of
pronation and foot type (Nawoczenski et al. 1998), a
study evaluating the influence of running shoes on
rearfoot pronation should probably also determine
each runner’s foot type to see if anatomical features
confound any effect due to shoes.
Gender may also influence running mechanics.
For example, it is often assumed that females have
wider pelves relative to height or leg length, and
that this causes them to have a greater Q-angle,
the angle between a line drawn from the anterior
superior iliac spine (ASIS) to the mid-patella and a
line from the mid-patella to the tibial tuberosity
(Atwater 1990). Individuals with a large Q-angle
are often assumed to be more susceptible to certain
types of knee injury (Atwater 1990; Messier et al.
1991). If a greater Q-angle increases susceptibility to
injury, and if females tend to have greater Q-angles
than men, then gender may be a risk factor. Messier
et al. (1991) did find a relationship between Q-angle
and patello-femoral pain, but also found that the
relationship was similar for both males and females.
As a further example, Nelson et al. (1977) found that
a group of elite male runners took strides longer
than those of a group of elite females over a range of
speeds when compared in absolute units. When
stride length was divided by leg length, relative
stride length for females was longer than the same
measure for men. This illustrates the importance of
looking at both absolute and relative stride length,
but since females are on average shorter than males,
it also suggests that caution should be taken to
ensure that any differences found are due to gender,
and not to differences in size.
Treadmill vs. overground running
Many biomechanical and physiological studies of
running are carried out indoors with subjects running on a treadmill since it is much easier to control
conditions in the laboratory and the space needed
is smaller. Many studies have examined the differences between treadmill and overground running,
often with contradictory results, but with a general
agreement that there are differences between the two
modes (van Ingen Schenau 1980; Nigg et al. 1995).
Nigg et al. (1995) found a systematic difference with
subjects landing on the treadmill with a flatter foot
position compared with overground running, but
also found inconsistent trends among individuals.
They concluded that assessing running kinematics
on a treadmill may lead to inadequate conclusions
about overground running. While overground vs.
treadmill differences are usually subtle, and it is
typical to apply findings from treadmill running to
more general situations, it should be kept in mind
that the use of the treadmill may have an influence
on results in ways that are not fully understood.
Kinematics of running
Kinematics provides one set of measurements that
are often used to identify differences between individual runners, groups of runners, or specified
conditions. Of primary interest are measures of the
displacement, velocity and acceleration of segments
of the body, though there are some areas of study
where movements of the centre of mass of the body
are of interest.
Whole body kinematics
Stride length (SL) is one of the most frequently studied
biomechanical measures. SL here will refer to the distance from one foot contact to the next contact of the
same foot, with step length defined as the distance
between successive footstrikes of different feet.
Velocity is determined by both SL and stride rate
(SR): V = SL × SR. As shown in the graphs in Fig. 8.1
the dynamics of running
163
Inset A
Vertical oscillation
9
Angle conventions
8
7
6
Lower extremity joint angles
130
Max. knee flex. sw.
Thigh
w/vert
110
Knee
Max. ankle dorsi. flex.
90
Ankle
Max. ankle pl. flex.
70
Degrees
Inset B
50
5
Max. knee flex. sup.
Max. thigh flex. w/vert.
30
4
3
Max. knee ext.
10
Stride length
(cm)
Stride rate
(cm)
2
0
–10
4
Max. thigh ext. w/vert.
6
8
10
Speed (m · s–1)
–30
Inset C
Stride length, stride rate
4
Left and right foot
temporal measures
Stride length (cm)
3
2
Stride rate (Hz)
LFS
1
LTO
L. support
RFS
RTO LFS
R. support
Temporal measures
800
L. non-support
Cycle time
R. non-support
Time (ms)
600
L. swing
Swing time
400
R. swing
Support time
200
0
3.5
Cycle time
Non-support time
4.0
4.5
5.0
5.5
6.0
Speed (m·s–1)
Fig. 8.1 Changes in kinematic variables with increased running speed for an example runner.
R. swing
164
locomotion
for an example runner, both SL and SR increase
linearly with speed over a range of distance running
speeds (Luhtanen & Komi 1978; Ito et al. 1983). Inset
B in Fig. 8.1 shows that at higher speeds SL begins to
level off, and may decrease, while SR increases proportionately faster than at slower speeds (Dillman
1975; Mero & Komi 1986). Plamondon and Roy
(1984) showed that SL, SR and other temporal and
spatial parameters were very dependent on speed
as sprinters accelerated over the first 18 strides of
a 100-m run. Stride length is often put relative to
leg length when comparing individuals to reflect
the effect body size may have on the length of the
stride, but correlational studies have generally
shown a weak and non-significant relationship between SL and leg length at distance running speeds
(Cavanagh & Kram 1989). Somewhat higher correlations between SL and leg length (r = 0.70) and
height (r = 0.59) have been found for sprinters
(Hoffman 1971).
Cycle time, the inverse of SR, decreases with
increased running speed, as does both the absolute
time and percentage of time spent in support. The
change in support time with speed is non-linear in
that decreases are greater at slower speeds than
at faster speeds. Both relative and absolute nonsupport times increase with increased running
speed, while the time the leg spends in swing
increases slightly at lower speeds but decreases
slightly at higher speeds (Nilsson et al. 1985). For
the subject shown in Fig. 8.1 the percentage of
time spent in support during a half-cycle decreased
from 80% at 3.6 m · s–1 to 66% at 6 m · s–1, with nonsupport time increasing from 20% to 34%. Ardigao
et al. (1995) had subjects run using a rearfoot strike
in some trials and a forefoot strike in other trials,
and found no significant differences in SL or SR
based on footstrike position at any speed over the
range 3.43 – 4.04 m · s–1.
Lower-extremity kinematics
thigh, knee and ankle
Figure 8.2 illustrates the patterns of movement that
occur in the lower-extremity joints during a running
cycle (using the angle convention shown in inset A
in Fig. 8.1). Figures 8.1 and 8.2 show how some
of these angles change with speed. The discussion
below is based on these and other data (Nilsson et al.
1985; Nigg et al. 1987). Prior to footstrike, extension
of the hip has begun, but there is a slight period of
flexion after the foot makes contact due to the forces
at impact, and the hip movement quickly resumes
extending (Nilsson et al. 1985). The knee joint shows
two periods of flexion, one during support and the
other during swing, with the flexion in swing serving to reduce the leg moment of inertia making it
easier to swing the leg through to the next footstrike.
Depending on the running style of a particular runner, the ankle may show a rapid plantar flexion
following footstrike, for a rearfoot striker, or may
begin to dorsiflex, for a midfoot or forefoot striker.
With increasing speed maximal hip flexion and
extension angles increase, as does the maximum
flexion angle of the knee during both the swing and
support periods. The angle of the thigh with the vertical at footstrike increases with increasing running
speed, and the angle of the knee at footstrike is less
extended at faster compared with slower speeds.
There is a less extended angle of the knee prior to
footstrike at higher speeds, and while the ankle
angle during the pushoff phase becomes slightly
more plantarflexed with increased running speed,
the maximal dorsiflexion angle during support does
not change much. Nigg et al. (1987) found that the
vertical component of the speed of the heel at footstrike increased with running speed, while the
horizontal component showed no change.
rearfoot pronation
The inward rolling motion at the ankle that occurs
as the foot goes flat just after footstrike has been
studied extensively in distance running because of
implied relationships between pronation about the
subtalar joint and lower extremity injuries. This
motion is often referred to as pronation and supination, as it will be here. Though three-dimensional
studies more completely describe the complex
movements occurring during pronation (Engsberg
1996; Nawoczenski et al. 1998), two-dimensional
analyses have been performed most often and the
measures obtained would more appropriately be
the dynamics of running
165
Lower extremity angles
Ankle
130
Dorsiflexion
110
90
Plantarflexion
70
Speed (m · s–1)
2.98
3.51
6.09
7.48
Knee
Degrees
120
Flexion
80
40
0
Extension
Thigh
60
Flexion
All curves are for left side
40
20
0
Fig. 8.2 Ankle, knee and thigh angle
changes throughout a running cycle
at four different running speeds for
an example runner.
Left-foot strike
Right-foot strike
–20
Extension
0.0
0.1
labelled eversion and inversion rather than pronation and supination (Taunton et al. 1985). Figure 8.3
shows typical angles for the leg, heel, and rearfoot
during a portion of the support period. The rearfoot angle at footstrike and at maximal pronation,
the amount of pronation, and the maximal pronation velocity have all been used to characterize the
pronation movement (Nigg 1986).
Table 8.1 shows rearfoot movement data from a
group of elite female distance runners and shows
the wide range of values that is typical. In this group
of runners, the least amount of pronation was for a
runner who actually never got beyond a neutral
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Time (s)
rearfoot position, with a maximal ‘pronation’ angle
that was still in 3° of supination. At the other end of
the spectrum was a maximum pronation value of
18°. In a similar group of elite male runners, running
at a slightly faster speed, a maximal pronation angle
as high as 24° was found. A variety of factors can
influence the amount of pronation that takes place
following footstrike, including anatomical structure, footwear, the placement of the foot at contact,
and the surface slope. Runners who land with a high
amount of supination can be more at risk for inversion sprains. Greater maximal pronation has been
associated with a less vertical angle of the leg and a
166
locomotion
Rearfoot pronation
Supination
10
Rearfoot angle
Leg angle
Heel angle
Footstrike
Angle (degrees)
Rearfoot angle
conventions
50 Time (ms)
–20
Rearfoot angular velocity
(degrees · s–1)
Pronation
100
Maximal
pronation
Total amount
of pronation
350
Leg
angle
Right
leg
Maximum
pronation
velocity
–420
Rearfoot
angle
Table 8.1 Rearfoot pronation values for elite female
distance runners at 5.36 m · s−1.
Mean
(SD)
Max.
Min.
N
Angle at
footstrike
(deg.)
Max.
pronation
(deg.)
Amount of
pronation
(deg.)
Max.
pronation
velocity
(deg. · s−1)
14.5
(−6.1)
30.2
2.6
47
−8.5
(4.3)
3.2
−18.6
47
23.0
(5.5)
38.8
12.6
47
−902
(280)
−437
−1563
26
less supinated rearfoot angle position at footstrike,
and greater pronation speed has been associated
with a more supinated rearfoot angle and a greater
angle of the heel with the vertical at footstrike
(Williams & Ziff 1991). Running with a greater
stride width—the horizontal distance between successive footstrikes—has been found to reduce pronation (Williams & Ziff 1991).
There is often an association assumed between
the nature of the arch of the foot and pronation, with
a flat foot assumed to be associated with more
pronation and a rigid high-arched foot associated
with less pronation. Nawoczenski et al. (1998) used
three-dimensional methods to assess the relationship between inversion–eversion and tibial medial
Heel
angle
Fig. 8.3 Leg, heel and rearfoot angle
curves during rearfoot pronation for
an example runner.
and lateral rotation, and found a ‘low rearfoot’
group (pes cavus) to show relatively more calcaneal
eversion compared with a ‘high rearfoot’ group (pes
planus), which showed more tibial rotation. The
influence of footwear on pronation, and the effect
excessive pronation may have on injuries, is discussed later.
Upper extremity and trunk
Vertical oscillation of the body has been shown to
decrease with running speed (Dillman 1975), as
shown in Fig. 8.1 for a marker on the head, and has
been reported to be as low as 4.7 cm at 9.8 m · s–1
(Mero et al. 1992). Runners tend to lean slightly forwards during the run, with values between 4 and
7 degrees for speeds up to 6 m · s–1. The trunk lean
angle has been found to increase slightly after foot
contact, increasing to as much as 12–13°, and then
decrease by the time toe-off occurs (Elliott & Roberts
1980; Elliott & Acklund 1981). Frishberg (1983)
reported a forward lean angle of 11.6° for a sprinter
at 9.2 m · s–1. Williams found trunk rotation range of
motion to average 24.3° at the hip and 26.7° at the
shoulder for a cycle of running at 3.6 m · s–1, with
considerable variability between subjects (Williams
1982). Lusby and Atwater (1983) found a greater
range of motion at the elbow and shoulder joints
the dynamics of running
with increased speed in female runners, with no
change in the sequence of movement in relation to
foot-ground events. The role of the arms, legs and
trunk in rotational movements during running have
also been examined using angular momentum
measurements (Hinrichs et al. 1983). About a vertical
axis, the angular momentum of the arms was found
to nearly balance the angular momentum of the rest
of the body, resulting in relatively low total body
angular momentum values throughout the running
cycle. Presumably the reciprocal action of the arms
in relation to leg motion has a role in optimizing
the energy associated with running, and support
for this premise comes from a study that showed
that Bo2 (submaximal oxygen consumption rate)
increased by 4% when the arms were constrained
to remain behind a runner’s body (Egbuonu et al.
1990).
Kinetics of running
Ground reaction forces and centre of pressure
The greatest musculoskeletal stresses in the lower
extremity occur during the support phase of running, and analysis of ground reaction forces can
provide insight into the factors that affect these
stresses. Figure 8.4 shows vertical, anteroposterior
and mediolateral force–time curves that are characteristic of a rearfoot strike and a midfoot or forefoot
strike. Table 8.2 shows data for peak forces and the
changes in speed, calculated from impulse data for
each of the three components of force, for 41 male
elite runners. Rearfoot strike patterns typically
show two vertical peaks, with the first peak sometimes referred to as the impact peak, influenced
primarily by the conditions at footstrike, and the
second maximum referred to as the active peak,
affected by muscle activity during support (Nigg
1986). Factors such as footwear, running speed, running surface and running style may affect whether
the first vertical peak is present or not. Runners who
land on the midfoot and forefoot typically show
either no vertical force impact peak or a much attenuated peak. During barefoot running Frederick and
Hagy (1986) found a greater first vertical force peak
to be significantly correlated with faster running
167
speeds, body mass, stature, step length, leg length, a
more plantarflexed ankle position at footstrike, and
a greater hip–foot horizontal distance at footstrike.
Combined, all these measures accounted for only
52% of the variability in the first vertical peak, indicating that there are other important factors besides
the ones they measured. A higher second peak was
significantly correlated with most of these same
factors, but not with running speed.
Anteroposterior (A-P) forces show a period of
braking during the first half of the support phase,
when the forward speed of the runner is slowed
down, followed by a propulsive phase where forward speed increases. For the speed of 5.96 m · s–1
shown in Table 8.2, the decrease in A-P speed represents a 5% change. The average net change in
velocity of 0.03 m · s–1 reflects the extra propulsion
needed to overcome air resistance during the flight
phase, and these values are similar to values found
by others (Munro et al. 1987). The net A-P impulse
values are also sometimes affected by the somewhat
artificial running conditions used in force platform
data collection. A sharp rise and fall in the A-P force
is often seen in a midfoot or forefoot striker, as
shown in Fig. 8.4. It has been more difficult to
explain the relationship between patterns of change
in the mediolateral forces with movements, though
Williams (1982) did find a correlation of 0.71
between the net mediolateral impulse and the position of the foot relative to a midline of progression.
The magnitude of vertical forces varies considerably between runners running at the same speed, as
can be seen in the data in Table 8.2. Cavanagh and
Lafortune (1980) showed a range of 2nd peak forces
from approximately 2.2 to 3.2 × body weight (BW)
from a group of 17 runners running at 4.5 m · s–1,
with a mean of 2.8 (±0.3) BW for rearfoot strikers
and 2.7 (±0.2) for midfoot strikers. When a force
platform is used to collect force data, the centre of
the pressure distribution under the foot can also be
determined. As shown in Fig. 8.4, this has been used
to identify the type of landing used by a runner,
employing a measure labelled strike index (SI), the
distance from the back of the heel to the location
where the first centre of pressure point is within
the shoe contact outline, measured as a percentage of shoe length (Cavanagh & Lafortune 1980).
Joint angles and angular velocity
(degrees)
500
0
–500
Thigh
Knee
Ankle
Dorsiflexion
Joint angular velocity
(degrees)
100
Plantarflexion
50
0
–25
Flexion
Extension
Joint angles
Joint force and net muscle moment
Sign of extensor moment
Hip: Positive
Knee: Negative
Ankle: Positive
Net muscle moment
(N·m)
250
0
–300
(N)
300
0
–250
Hip
Knee
Ankle
A-P joint force
–500
Vertical joint force
(N)
2000
1000
–300
Ground reaction forces
2500
(N)
(N)
Vertical
0
200
Anteroposterior
–300
150
Mediolateral
(N)
–50
0.7
0.8
1.0
1.2
1.4 1.1
Strike index=10%
1.2
1.4
1.6
1.8
Strike index = 50%
Centre
of
pressure
Heel strike
Midfoot strike
Fig. 8.4 Ground reaction forces, and lower-extremity joint forces, muscle moments, joint angles and joint angular velocity
for an example runner.
the dynamics of running
169
Table 8.2 Vertical, anteroposterior (A-P) and mediolateral (M-L) ground reaction force peaks and change in velocity data
for elite male distance runners at 5.96 m · s−1 (N = 41).
Mean
(SD)
Max.
Min.
Vertical Vertical
Vertical
1st peak 2nd peak ∆V
(BW)
(BW)
(m · s−1)
A-P peak
braking
(BW)
A-P peak
Propulsion
(BW)
A-P ∆V
braking
(m · s−1)
A-P ∆V
Propulsion
(m · s−1)
M-L peak
(medial)
(BW)
M-L peak
(lateral)
(BW)
M-L net
∆V
(m · s−1)
2.83
(0.49)
4.16
1.41
−0.891
(−0.148)
−1.335
−0.630
0.539
(0.065)
0.390
0.670
−0.284
(−0.044)
−0.378
−0.185
0.255
(0.050)
0.015
0.315
0.344
(0.117)
0.620
0.115
−0.410
(0.316)
−0.088
−2.233
0.049
(0.072)
0.275
−0.145
3.13
(0.19)
3.48
2.72
1.42
(0.17)
1.72
0.83
BW, Body weight.
Cavanagh and Lafortune found 12 of their runners
to show a rearfoot strike pattern (SI average = 17%),
landing with an average of 10.4° of foot abduction.
Similar values for the five midfoot strikers were 50%
and 5.3°. The first vertical force peak for the rearfoot
strikers averaged 2.2 (±0.4) BW. Unpublished data
from the present author show a mean SI of 40.1%
(±20.4%) for a group of elite female distance runners
running at 5.36 m · s–1, with a range from 6% to 76%.
As running speed increases the magnitude of the
vertical ground reaction force increases, as does
the rate of loading, and initial contact with the
ground tends to occur further forwards on the
foot (Frederick & Hagy 1986; Mero & Komi 1986;
Munro et al. 1987; Nigg et al. 1987). The magnitude
of A-P forces increases with increased running
speed, as does the A-P impulse, reflecting a greater
decrease and then increase in forward speed during
the support phase (Munro et al. 1987).
Joint forces and moments
By combining information from segmental kinematics, ground reaction forces, centre of pressure,
and body segment parameters, estimates can be
made of the internal joint reaction forces and net
muscle moments at each joint in the lower extremity
using the methods of inverse dynamics. Examples
of these moments and forces during a running cycle
for the hip, knee and ankle joints are shown in
Fig. 8.4, and other examples are present in the literature (Mann & Sprague 1980; Winter 1983; Putnam &
Kozey 1989; Scott & Winter 1990; Prilutsky et al.
1996).
The knee and ankle show extensor moments
throughout most of the support period, while the
hip moment is extensor in the first half of contact
and may become a flexor moment later in support as
the leg begins forwards in the swing phase of the
running gait. There are a number of differences in
the moment patterns immediately after footstrike
between rearfoot and midfoot strikers. During the
30 ms after the rearfoot strike shown in Fig. 8.4 the
hip shows an extensor moment, the knee a flexor
moment, and the ankle a net moment of zero.
Absent from this example, but present for some
other runners, is a small dorsiflexor ankle moment
immediately after footstrike when the tibialis anterior muscle acts eccentrically to ease the foot down.
In the midfoot pattern, the extensor hip moment
and the flexor knee moment immediately drop
towards zero after foot contact, while the ankle
shows an immediate extensor moment. Komi (1990)
used direct force measures to show that there was a
sudden unloading of the Achilles tendon immediately after a heel-first footstrike, with no such
change in a midfoot landing, and these results are
consistent with the patterns shown in Fig. 8.4.
Following footstrike, when the knee flexes as the hip
extends, there is likely to be eccentric muscle action
in the knee extensors, though the true muscle length
changes for multijoint muscles cannot be determined solely from joint angle changes and would
have to be estimated from a more sophisticated
model than was used here. The small positive spike
in the A-P force in Fig. 8.4 following footstrike in the
rearfoot strike pattern is reflected in the short positive A-P joint force seen at the hip, knee and ankle
170
locomotion
following contact. These forces quickly turn negative, but show another sharp change in magnitude a
short time later. Vertical joint reaction forces show
patterns that parallel vertical ground reaction force
changes, with the magnitude of the force gradually
decreasing the more proximal the joint. The short
dashed vertical lines shortly after footstrike in the
rearfoot strike example in Fig. 8.4 designate the time
when the foot goes flat, and it can be seen that there
is a sharp change in each of the other force and
moment curves at this time.
individual muscle and
segmental forces
The ability to quantify individual force contributions from muscle and other soft tissues would
greatly enhance the ability to identify relationships
between movement, force and injury. However,
because of the invasive nature of direct measures
of muscle force, it is seldom undertaken. Direct
measurements have been made using a surgically
implanted tendon buckle to measure Achilles tendon forces during running (Komi 1990). For a subject running over a range of speeds, a maximal
loading of 12.5 × BW was found for Achilles tendon
force at an intermediate speed of 6.0 m · s–1, with
different maximal magnitudes found in other subjects. When given relative to tendon cross-sectional
area the resulting stress value was higher than
reported values for single-load maximum tendon
strength. Komi also found that the rate of loading
of the Achilles tendon increased with increased
running speed throughout a range of speeds tested
up to a maximum speed of 9 m · s–1.
An alternative method for estimating internal
forces is to use musculoskeletal models to predict
forces, but these methods may include errors due to
the assumptions that have to be made. Forces in the
Achilles tendon have been estimated to range from
5 to 10 times BW with ankle bone-on-bone forces
ranging from 8.7 to 14 BW (Burdett 1982; Scott &
Winter 1990). A model predicting internal forces
gave ranges of 4.7– 6.9 BW for peak patellar tendon
force and 1.3 –2.9 BW for plantar fascia force (Scott
& Winter 1990). As with individual muscle forces,
little information is available identifying direct
bone or joint loading patterns in the lower extremity
during running. Burr et al. did measure strain and
strain rates in the tibia in vivo during running (Burr
et al. 1996), and such studies may provide further
insight into the mechanisms of stress-related injuries.
Electromyographic patterns during running
Examples of electromyographic (EMG) activity in
several lower-extremity muscles during running
are shown in Fig. 8.5, and further examples can be
found in the literature (Nilsson et al. 1985; Putnam &
Kozey 1989; Prilutsky et al. 1996). During swing
there is steady activity in the tibialis anterior that
continues through footstrike, perhaps to provide
stability at impact through co-contraction with the
triceps surae muscles. The biceps femoris and gluteus maximus both show a period of activity in the
time period before footstrike, acting eccentrically to
slow the flexion of the hip and extension of the knee.
At footstrike there is activity in all the primary
muscles that provide extensor support during the
contact phase—the gluteus maximus, rectus femoris,
vastus lateralis, and gastrocnemius. The gastrocnemius activity during support helps to provide the
torque needed to plantarflex the ankle during late
support through toe-off, and activity in the biceps
femoris in late support may help begin the flexion of
the knee that occurs during the flight phase. Rectus
femoris activity during the swing phase may help
both with flexion of the hip and extension of the
knee. At a speed of running of 8 m · s–1 Nilsson et al.
found a phase shift in the onset of activity in the gluteus maximus, quadriceps and hamstring muscles,
with EMGs turning on sooner in the swing phase
before footstrike. Between 4 and 8 m · s–1 they also
found greater rectus femoris activity during swing,
aiding in hip flexion, than was found during the
support phase.
With increased running speed the magnitude of the
EMG signals increases in the lower-extremity muscles
(Nilsson et al. 1985; Mero & Komi 1986). The absolute duration of activity decreases due to the shorter
cycle time associated with increased speed, but peak
EMG, overall integrated EMG, and the relative duration of activity as a percentage of cycle time increase
with increased speed. van Ingen Schenau et al. (1995)
the dynamics of running
171
Lower extremity angles
Dorsiflexion
Ankle
110
90
All curves are for left side
Plantarflexion
70
Angle (degrees)
120
Flexion
Knee
80
40
Extension
0
Flexion
Thigh w/vert
40
20
0
Extension
–20
Left-foot
strike
Right-foot
strike
Speed + 3.51 m ·s–1
Left-foot
strike
EMG activity
0
Gluteus maximus
0
Biceps femoris
Arbitrary units
0
Rectus femoris
0
Vastus medialis
0
Medial gastrocnemius
0
Tibialis anterior
Fig. 8.5 Lower-extremity angles and
EMG patterns for six muscles during
a cycle of running for an example
runner.
0
0.0
0.1
0.2
0.3
0.4
Time (s)
0.5
0.6
0.7
0.8
172
locomotion
examined lower-extremity muscles in running and
concluded that monoarticulate muscles show activity primarily during periods when they are shortening, and are not very active in eccentric muscle
work, similar to results found for cycling.
Measures of mechanical power
Mechanical power output during running has been
measured for many years, but there still is a great
deal of confusion over which methods are best
to use (Winter 1979; Williams & Cavanagh 1983;
Aleshinsky 1986a; van Ingen Schenau & Cavanagh
1990). One of the ‘problems’ with measuring the
external work done in a cyclic activity such as running is that for constant-speed level running the
total external work done in a running cycle will be
zero, yet there is obvious metabolic energy expenditure involved. The mechanical work done during
running has been derived using three general
methods, based on:
1 changes in energy levels of the body centre of mass;
2 changes in segmental energy levels derived from
kinematics; and
3 changes in segmental power derived from joint
forces and moments.
The latter method appears to have advantages over
the other two (Aleshinsky 1986a; Putnam & Kozey
1989; van Ingen Schenau & Cavanagh 1990). Different methods of measuring mechanical power
during running using a segmental energy approach
have yielded results that show up to a 10-fold difference in power for a given level of effort (Williams &
Cavanagh 1983).
Aleshinsky (1986b) and van Ingen Schenau and
Cavanagh (1990) proposed methods that they
believed better addressed some of these methodological problems, but acknowledged that even the
proposed methods leave a number of problems
unresolved and rely on assumptions that may have
major deficiencies. Among the problems (Williams
& Cavanagh 1983; Aleshinsky 1986a; van Ingen
Schenau & Cavanagh 1990) inherent in calculating
mechanical power during a cyclic activity such as
running, where the primary work done is to support
the body during each foot contact phase, are:
• limitations in identifying the amount of energy
transferred between segments;
• inability to determine the exact source of positive
mechanical power;
• the capability to calculate only net muscle
moments;
• lack of knowledge of the full role of muscles that
cross more than one joint; and
• inability to quantify precisely the effect of stretch
–shortening cycle contributions on the work done.
The usefulness of measures of mechanical work will
be somewhat limited until we better understand
some of these factors.
Biomechanics in relation to performance
Most biomechanical studies of running are performed in controlled experimental situations rather
than during competition, making the direct association of biomechanical parameters with performance difficult to obtain. Usually it is only possible
to obtain kinematic information in competitive
situations, limiting the information available, and
often the movement patterns in competition are
influenced by strategy or the presence of other runners, making it difficult to isolate the importance of
biomechanical factors to performance. As a result,
most information relating biomechanics to performance comes from either studying factors that are
related to performance, such as submaximal oxygen
consumption in distance running, or by examining
characteristics of different levels of runners in the
laboratory and identifying either significant differences in biomechanical measures between groups,
or finding strong correlations between performance
times and biomechanical indices.
Several studies have compared ‘elite’ distance
runners with ‘good’ runners, often with equivocal
results. Compared with good runners, elite runners
have been found to have a longer stride length
(SL) at a given speed in distance running (Dillman
1975) and in sprinting (Kunz & Kaufmann 1981),
though another study found shorter SLs (Cavanagh
et al. 1977). Cavanagh et al. (1977) found no significant differences in the angles of the thigh with the
vertical or the knee angle at various times throughout a running cycle between groups of elite and
good male runners. They did find the good runners
to plantarflex the ankle 8° more than the elite runners during toe-off. Net muscle torques during the
the dynamics of running
swing phase of running did not show differences
between groups, and while there were no differences in vertical oscillation between the groups, the
elite athletes did show a more symmetrical vertical oscillation pattern between left and right sides
compared with controls.
In another study, an elite group of female runners
was found to show a foot contact position further
forward on the shoe compared with a control group
of good runners at the same speed of running
(Williams et al. 1987). The elite runners also had
lower first and higher second vertical force peaks,
a larger change in vertical velocity, a higher peak
braking anteroposterior force, higher laterally directed mediolateral forces, and a shorter support
time. The elite runners had narrower pelvises than a
student population of similar age, and were shorter
in stature, lighter and had less iliac crest fat than a
typical non-athletic female population.
Biomechanical factors and
running economy
Running mechanics are often studied in relation to
submaximal oxygen uptake per unit body mass
(Bo2), often termed running economy. Energy
expenditure in running will have a direct affect on
performance, and anything that will improve economy should have a beneficial effect on performance. If changes in movement patterns result in
reduced energy costs, the reduced cost should allow
an individual to either maintain a given level of performance for a longer period of time, or to raise the
level of effort that can be sustained over a fixed time
or distance. In distance running a small improvement in economy can yield substantial benefits.
A 1% improvement in a world-class 10 k race yields
a 16 s faster time, putting the runner 100 m ahead
of where he or she would otherwise finish.
Variations in Fo2
The variation in economy among runners at the
same speed is substantial, with typical variations
exceeding 15% and ranging as high as 30%
(Williams & Cavanagh 1983; Daniels 1985). Many
studies have shown a general linear relationship
between economy and speed in running (Daniels
173
1985; Morgan et al. 1989). Economy among a group
of subjects running at the same speed is not highly
correlated to the stride length (SL) each runner
chooses (Brisswalter et al. 1996). However, Bo2 for
a given individual does vary with SL, usually being
minimum at the freely chosen SL and increasing at
shorter or longer SLs (Cavanagh & Williams 1982).
Morgan et al. (1994) demonstrated that it was possible to train runners who chose an uneconomical
SL to run at an SL closer to the one predicted to be
optimal, with a concomitant lowering of Bo2.
To test the sensitivity of economy to changes in
biomechanical variables, Egbuonu et al. (1990) performed a study where runners deliberately: (i) used
increased vertical oscillation; and (ii) ran with their
arms behind their backs. While both protocols
increased Bo2 above that for their normal running
pattern, by 4% and 4.6%, respectively, the increases
were relatively small (~1.6 ml · kg –1 · min–1), and it
was suggested that these might be upper limits to
changes in economy that result from changes in
mechanics. Another study in the same laboratory
trained four runners with feedback intended to
improve economy (Miller et al. 1990). The subjects
given feedback significantly reduced Bo2 compared
with pretraining measures, with reductions that
were 0.6 ml · kg–1 · min–1 lower than the reduction
found for a control group.
Mechanical power
Submaximal oxygen uptake is a global measure of
energy expenditure, and it might be expected to be
related to the global measure of total body mechanical work during running. Studies examining the
relationship between power and economy across
speeds do find strong correlations between metabolic
energy costs and mechanical measures of power
(Shorten et al. 1981). However, strong relationships
have not been found between these two measures at
any given speed of running, and the lack of a clear
association may be in part due to difficulties associated with the methods used to calculate mechanical
power, as discussed earlier. At a given running
speed, several studies have shown weak trends towards better economy in running being associated
with lower mechanical power (Williams & Cavanagh
1987) or total lower body angular impulse (Heise
174
locomotion
& Martin 1990), but others have found no specific
relationship.
Biomechanical measures
A variety of biomechanical measures describing
running mechanics have been identified as being
related to better economy, but there are many inconsistencies among studies. Better economy has been
associated with:
• less extension at the hip and greater extension at
the knee during toe-off, more dorsiflexion, and a
greater decrease and subsequent increase in forward velocity during support (Williams et al. 1987);
• a higher first vertical force peak, a greater angle of
the shank with the vertical at footstrike, less plantar
flexion at toe-off, greater forward trunk lean, and a
lower minimum velocity of a point on the knee during foot contact (Williams & Cavanagh 1987);
• a longer support time, lower medially directed
ground reaction force, greater extension of the hip
and knee at toe-off, and a faster horizontal velocity
of a point on the heel at footstrike (Williams &
Cavanagh 1986); and
• less arm movement (Anderson & Tseh 1994).
Ardigao et al. (1995) found no differences in economy in runners when they ran with a rearfoot strike
pattern compared with a forefoot strike pattern.
Until more consistent relationships are established
the relationships described here should be considered tentative and may not be useful as the basis for
altering someone’s mechanics to improve economy.
Stretch– shortening cycle
A process that has often been cited as a major
contributor to the work done in running, and
consequently as a mechanism that reduces energy
expenditure by muscles, is the stretch–shortening
cycle of muscle use involving elastic tissues in the
muscle, tendon and arch of the foot (Williams 1985b;
van Ingen Schenau & Cavanagh 1990; Taylor 1994;
van Ingen Schenau et al. 1997). The work done as
a result of the stretch–shortening cycle is often
attributed to the storage and reutilization of elastic
energy, but there are other factors that have been
proposed as being as important or more important,
including: increasing the time available for force
production; potentiation of the contractile mechanism during the concentric phase of the movement;
and triggering of spinal reflexes (Williams 1985b;
van Ingen Schenau & Cavanagh 1990; van Ingen
Schenau et al. 1997). Stretch–shortening mechanisms
are often used to explain the high (40 –70%) efficiency rates often calculated for running (Anderson
1996; Williams & Cavanagh 1983). There seems to
be general agreement that economy benefits from
stretch–shortening mechanisms, with the mechanical
work attributable to stretch–shortening sources reducing the amount of metabolic work done by active
muscles (Williams 1985b; van Ingen Schenau &
Cavanagh 1990; Taylor 1994). For a more detailed
discussion of the issues involving the stretch–
shortening cycle see the special issue on the subject
in the Journal of Applied Biomechanics (Vol. 13, 1997).
Flexibility
Several studies have examined the influence of lowerextremity flexibility on economy. One study found
that increased flexibility after a period of flexibility
training was associated with better running economy
(Godges et al. 1989). However, other studies have
shown economy to be better in individuals with less
flexibility (Gleim et al. 1990; Craib et al. 1996), with
increased contribu-tions from stored elastic energy
cited as the likely mechanism.
Body mass and distribution of mass
Measures of Bo2 are usually given relative to body
mass (i.e. as ml · kg–1 · min–1), but often there is
still an influence of size on economy beyond simple
scaling to body weight. Moderate correlations have
suggested that better economy is associated with
runners with greater mass (Anderson 1996; Williams
& Cavanagh 1986; Williams et al. 1987; Bergh et al.
1991). Since Bo2max has also been shown to be lower
in runners with greater mass (Bergh et al. 1991),
there may be no advantage to the lower Bo2 in
heavier runners since the percentage of Bo2max may
be similar for both light and heavy runners.
Some have proposed that differences in mass distribution among the segments might be related for the
inverse relationship between economy and body
weight (Cavanagh & Kram 1985; Pate et al. 1992).
the dynamics of running
When weights are added to the extremities there is
an increase in metabolic energy costs, indicating that
mass distribution can affect Bo2 (Catlin & Dressendorfer 1979; Martin 1985), but any effect due to actual
differences in mass distribution among athletes has
not been demonstrated. Taylor (1994) found little difference in energy consumption among similar sized
animals with very different limb mass distribution.
Air resistance
Air resistance plays a smaller role in the work done
during running than in other sports where speed
is higher, such as cycling or speed skating. Pugh
(1971) found the extra oxygen consumed while running against a wind increased relative to the square
of wind velocity. While he predicted the overall
energy cost of overcoming air resistance in track
running to be approximately 8% at a distance speed
of 6 m · s–1 and 16% at sprint speeds (10 m · s–1),
Davies (1980) predicted somewhat lower values
(7.8% at 10 m · s–1, 4% at 6 m · s–1, and 2% at
marathon speeds). Running behind other com-
175
petitors provides shielding from air resistance and
reduces drag and metabolic costs (Kyle 1979).
Running in a pack has been predicted to reduce
air resistance by 40 – 80%, depending on how close
one runner follows another, lowering oxygen costs
by 3 – 6% (Pugh 1971; Kyle 1979).
Biomechanical factors and injury
As running has increased in popularity over the last
20 years as a form of exercise, so have injuries to
runners. The wide variety of methods used to compile injury data make it difficult to identify the true
incidence of injury, but van Mechelen (1992) found
rates from 37 to 56% in studies of more than 500 subjects. Table 8.3 summarizes the results from several
epidemiological studies that attempted to identify
the source of lower-extremity injuries in running. It
should be noted that the methods used to collect
injury statistics and the specific population sampled
can have a major effect on results, and such factors
may account for some of the large differences seen
in the studies in Table 8.3.
Table 8.3 Common injury sites in running.
Study
James et al.
(1978)
Clement et al.
(1981)
Ballas et al.
(1997)
Bennell and
Crossley (1996)
Bennell and
Crossley (1996)
Type of subjects
Runners
Runners
Runners
Runners
Sprinters
No. of injuries
180
1650
860
39
19
Type of data
Clinic
Clinic
Clinic
Interview
Interview
29.0
13.0
25.8
13.2
13.8
7.8
15.0
13.6
14.0
5.0
11.1
7.0
6.0
4.7
2.2
4.0
6.0
5.8
2.6
3.2
4.3
4.5
9.3
13.9
25.1
6.0
18.0
4.3
38.0
8.9
3.0
Site of injury (%)
Knee pain
Shin splints–tibial stress
syndrome
Achilles tendinitis
Plantar fasciitis
Ankle/foot tendinitis
Stress fracture
Tibial stress fracture
Metatarsal stress fracture
Iliotibial tract tendinitis
Patellar tendinitis
Hamstring strain
Adductor strain
Ankle lateral ligament sprain
Others
5.0
3.8
2.2
5.2
6.0
4.9
9.4
176
locomotion
This section will consider only scientific studies
that have attempted to relate biomechanical and
anatomical factors to different types of injury, and
will not try to provide a detailed description of typical injuries, nor will it provide information about
how best to treat injuries. There are many good articles and books dealing with sports medicine that
provide this type of information. There is a paucity
of good scientific studies showing definitive relationships between either anatomical factors and
injury, or biomechanical measures and injury. The
relationships described in the paragraphs below
should be viewed as tentative relationships until a
stronger body of literature is available to confirm
them.
Knee pain
Epidemiological studies of running injuries find
the knee to be the most frequent site of injuries
(Clement et al. 1981; Maughan & Miller 1983) with
chondromalacia patella, pain on the undersurface of
the patella, as one of the most frequent knee injuries.
Rearfoot pronation has often been cited as a primary
cause of this type of knee pain, with the internal
rotation of the patella that accompanies rearfoot
pronation causing the patella to be pulled laterally,
increasing the pressure exerted on the undersurface
of the patella (James et al. 1978). Nigg et al. (1984)
did find greater pronation in runners with tibial
tendinitis compared with runners who felt no
pain. However, Landry and Zebas (1985) found
no significant relationship between the incidence of
knee pain and several different range of motion
measurements, including maximal pronation angle,
Q-angle and tibial torsion. While Messier et al. (1991)
also found no relationship with pronation, they did
find Q-angle to be a strong discriminator between
injured and non-injured subjects, along with several
ground reaction force variables.
Shin splints
The term ‘shin splints’ has been used to describe
pain in the anterior or medial portion of the tibia.
Several studies (Gehlsen & Seger 1980; Viitasalo &
Kvist 1983; Messier & Pittala 1988) have found
that runners with a history of shin splints showed
greater pronation and/or pronation speed compared with control groups.
Achilles tendinitis and plantar fasciitis
In the foot and ankle, Achilles tendinitis and plantar
fasciitis have been associated with both anatomical
and movement factors. Excessive pronation has
been implicated as a potential causative factor in
both these injuries (Clement et al. 1984b). Nigg et al.
(1984) found that runners with Achilles tendon pain
had greater maximal pronation angles, as well as
higher maximal vertical impact forces, but Messier
and Pittala (1988) found no relationship between
plantar fasciitis and rearfoot pronation or ground
reaction force measures. Training errors have been
found to be a primary factor in Achilles tendinitis
(in 75% of cases), and the injury is often associated
with moderate or severe subtalar or forefoot varus
(in 56% of cases) (Clement et al. 1984b). Plantar
fasciitis has paradoxically been found to be associated with both a flat foot and with a rigid cavus
foot, and it has also been linked to a tight Achilles
tendon (Warren 1990) and a greater plantarflexion
range of motion in the ankle joint (Messier & Pittala
1988).
Stress fractures
Stress fractures result from repetitive loading of
bone at levels higher than can be sustained without
a gradual breakdown of the involved tissues.
Stresses in the bone result from the ground reaction
forces applied to the feet, the internal muscle forces
caused by muscle contraction, and stress effects
resulting from the specific composition and orientation of the bones and joints in the lower extremity.
Table 8.4 lists some of the common sites for stress
fractures in runners. Ting et al. (1988) found no consistent anatomical variations or any ground reaction
force patterns that differentiated a relatively small
group of runners with previous navicular stress
fractures from a control group. Several studies have
associated a high-arched foot with a greater incidence of stress fractures (Giladi et al. 1985), and one
study found more femoral and tibial stress injuries
the dynamics of running
177
Table 8.4 Stress fracture sites in runners.
Study
Hulkko and
Orava (1987)
Sullivan
et al. (1984)
Brunet
et al. (1990)
Type of subjects
Athletes
(72% runners)
Runners
Runners
No. of injuries
368
57
139
Type of data
Clinic
Clinic
Self-report
49.5
19.8
12.0
6.2
4.1
43.9
14.0
21.1
3.5
43.9
34.7
Included in tibial
4.2
5.3
8.3
10.5
7.0
9.0
–
Site of injury (%)
Tibia*
Metatarsals
Fibula
Femur
Sesamoids
Calcaneus
Navicular
Pelvis
Others
2.4
1.9
4.1
* Includes fibular stress fractures in Brunet et al. (1990).
in high-arched feet and more metatarsal stress fractures in individuals with low arches (Simkin et al.
1989).
Muscle activity can modify the stress distribution
in the foot. Sharkey et al. (1995) hypothesized that
a consequence of fatigue during repetitive exercise might be an increase in the loading of the
metatarsals, and thus be a factor in the mechanism
of stress fractures. Using a cadaveric model they
showed that the addition of simulated muscular
contributions from the flexor hallucis longus
reduced dorsal strain on the 2nd metatarsal, and
simulated contraction of the flexor digitorum
longus reduced plantar-dorsal bending stress.
lists a number of factors that have been implicated
in the aetiology of hamstring strains but little scientific evidence exists to prove or disprove their
involvement. Sprinters with a history of hamstring
injuries have been found to have tighter hamstrings
compared with runners with no hamstring injuries,
as shown by a reduced range of motion at the hip
joint (74.1° vs. 67.2°) ( Jönhagen et al. 1994). They
could not identify whether these differences were
cause or effect. This study also reported that previously injured sprinters had lower hamstring and
quadriceps concentric torques at 30° · s–1, but not at
higher speeds of movement.
Muscle damage and soreness
Hamstring strain
Another common running injury, particularly for
faster sprinting speeds, is the hamstring strain
(Agre 1985). The injury is usually assumed to occur
near the end of the swing phase when the lengths of
the hamstring muscles are near their longest (Frigo
et al. 1979), and when the muscle action changes
from eccentric to concentric (Agre 1985). Agre (1985)
Runners often experience muscular pain following
prolonged downhill running, and the cause of the
damage to muscles is thought to be due to the
greater amount of eccentric muscle action that
occurs when running downhill. Dick and Cavanagh
(1987) found a 10% upward drift in Bo2 during
downhill running and a 23% increase in lowerextremity EMG. They hypothesized that damage
178
locomotion
to muscles and localized muscular fatigue cause
the recruitment of more motor units, contributing
to the increase in Bo2. There is evidence that running downhill changes the kinematics of running, as
shown by a more flexed knee position at footstrike
in downhill compared with level running, and a
greater maximal knee angle during support (Eston
et al. 1995).
Leg length discrepancy
A difference in length between right and left legs
has often been implicated as a factor in running
injuries. McCaw (1992) found greater ground reaction force loading in the long leg of a subject who
showed a leg length difference. After reviewing
the literature, he concluded that while there was
no unequivocal demonstration of an association
between leg length inequality and increased risk of
overuse injuries, neither is there reason to reject
the relationship. Friberg (1982) concluded from an
epidemiological study that leg length asymmetry
predisposed military recruits to stress fractures, but
Messier et al. (1991) found no relationship between
leg length inequality and patellofemoral pain.
Changes in biomechanics of running
with fatigue
As the muscles fatigue during the course of a run,
changes often occur in the kinematics, kinetics and
patterns of muscle use. A common problem in studies examining fatigue is that running speed usually
changes when a runner fatigues, and since most
biomechanical variables also change with speed, it
can be difficult to identify the changes due to fatigue
and those due to the altered speed.
Changes with fatigue have not been consistent
among studies. Elliott and Acklund (1981) found a
decreased running velocity, a shorter SL, a more
extended lower limb, and a slower backward velocity of the foot at footstrike during a fatiguing 10 000
m run. It was not clear whether the biomechanical
changes were due to fatigue or the slower speed. In
a 3000 m run where speed was controlled, Elliott
and Roberts (1980) reported non-significant trends
towards decreased SL and increased SR, increased
support time and decreased non-support time, a
significantly less vertical lower leg angle at footstrike, a less extended thigh at toe-off, and greater
forward lean near the end of the run compared with
three other time periods earlier in the run. Others
have found SL to increase with fatigue in both overground and treadmill running (Cavanagh et al. 1985;
Williams et al. 1991), with most subjects showing
a steady increase in SL but some not showing an
increase until late in the fatiguing run. One of these
studies found only a few trends for changes with
fatigue across a group of runners, reporting an
increase in maximal knee flexion during the swing
phase and greater hip flexion with fatigue (Williams
et al. 1991). They also found that changes in specific
measures were at times large for individuals.
As with distance running, fatigue studies of
sprinters are also complicated by differences in
speed, with measures usually collected initially
after maximal speed is attained and again near the
end of a run. The decreased velocity that usually
occurs with fatigue results in a decrease in SL and
SR (Bates et al. 1977), and it is also linked to an
increase in support time and decreases in the hip
and knee range of motion, with the specific changes
variable between subjects (Chapman 1982).
Biomechanical factors and
footwear/orthotics
During the late 1970s and early 1980s there was a
dramatic evolution of the design and materials used
in running footwear, and that trend has continued
throughout the 1990s as more sophisticated construction techniques have been developed and
advances have been made in the materials used in
footwear construction. Many of the advances made
in footwear design were a consequence of basic
information resulting from biomechanical studies
of the interaction between running mechanics and
footwear.
Running shoes and economy
A number of studies have demonstrated that the
design and materials used in footwear construction
can affect running economy. While the changes in
the dynamics of running
Bo2 are not large, studies have shown a change of
from 0.9% to 3.5% in submaximal energy costs.
Heavier shoes have been found to increase oxygen
cost by 1.9% per 100 g mass difference per shoe
(Catlin & Dressendorfer 1979), and when mass is
added to shoes, by 1.2% (Frederick et al. 1984) and
1.4% (Martin 1985) per 100 g per shoe.
Shoes with different cushioning properties have
also been found to affect Bo2, with shoes having
more cushioning usually being associated with
lower oxygen consumption (Frederick et al. 1983),
though some contrary results have been found,
as in a study where soft-soled inserts with very
high-energy-absorption characteristics resulted in
increased Bo2 (Bosco & Rusko 1983). The authors
suggested that the increased support time that
resulted from the soft inserts may have altered the
stretch–shortening cycle of events and reduced elastic contributions to the work done. Frederick et al.
(1983) found a significant correlation between Bo2
and maximum knee flexion velocity following footstrike, with the greater velocities found for harder
shoes cited as a possible reason for the increased
energy costs. It has been hypothesized that orthotic
devices might reduce oxygen consumption by altering lower-extremity mechanics and reducing muscular activity, but the trend across several studies
is for a slight increase, perhaps due to the added
weight of the orthotics (Clement et al. 1984a).
Jørgensen (Jørgensen 1990) examined Bo2 and
triceps surae and quadriceps muscle EMGs when
runners used a regular shoe and an identical shoe
with the heel counter cut out, expecting the heel
counter to have an effect on foot stability and
muscle use. He found reduced oxygen consumption
and lower EMG activity at footstrike when the heel
counters were in place, providing some support
for the hypothesized relationship between stability
and economy. In the early 1990s many shoes were
touted as having enhanced energy return capabilities, where a runner would take advantage of
a spring-like effect as energy stored during foot
impact help to propel the runner at toe-off. Shorten
(1993) presented convincing data that suggested
that the influence this might have on running
economy would likely be less than 1%, making it
unlikely that energy return by shoes would be
179
a major factor in altering the metabolic costs of
running.
Running shoes and running mechanics
The effect of footwear on the biomechanics of running has also been investigated widely. By varying
the design and materials in footwear, a variety of
changes to running mechanics can be effected.
Clarke et al. (1983b) found rearfoot pronation to be
greater when softer midsole materials were used
and in shoes with less rearfoot flare on the medial
side of the shoe, but found heel height to have no
effect on pronation. Others found an increase in the
amount of pronation going from a softer (25 durometer, shoe A) to a harder (35 durometer) midsole material, and they also showed an increase in
pronation velocity in stiffer shoes (Nigg et al. 1986).
They suggested that a softer material be placed in
the lateral heel to aid in shock absorption and firmer
material be used in the medial heel area to help limit
pronation, and concluded that increased lateral
flare would lead to an increase in pronation. Shoes
have also been found to decrease the maximal
pronation angle compared with a barefoot condition (Nigg et al. 1984).
While running in racing shoes may have an
advantage to oxygen consumption because of the
lower Bo2 associated with a lighter shoe, one of the
possible detriments is thought to be less stability.
Hamill et al. (1988) found greater pronation in racing
shoes (13.4°) compared with training shoes (7.8°),
and while running in training shoes caused an average increase of 1.3% in Bo2, differences were not
significant. Orthotics have been found to reduce
rearfoot pronation and pronation velocity (Taunton
et al. 1985; Smith et al. 1986), but Taunton et al. found
no change in knee internal rotation when an orthotic
device was used by overpronating runners. Nigg
et al. (1986) found the position of a medial support
wedge in a shoe could help limit the amount of
pronation.
Running shoes and injuries
Many associations have been made between the
impact shock that occurs in running and injuries,
180
locomotion
but there is little, if any, direct evidence that identifies specific mechanisms (Frederick 1986). Some
studies have shown a relationship between rearfoot
pronation and a variety of knee, leg and foot injuries,
as described in an earlier section. There are also
studies that have shown how footwear can help control pronation, so it is likely that footwear can have a
substantial influence on susceptibility to injury.
Shoe design and materials have an obvious effect
on the shock-absorption abilities of shoes, but the
wide range often seen in drop-impact tests generally does not correlate well to measures of impact
loading on runners assessed using force platform or
accelerometer measures (Clarke et al. 1983a; Nigg et
al. 1986). This may at least partly be because individual runners may adapt differently to a given shoe.
Shoes may cause runners to adjust kinematically, as
found in a study by Clarke et al. (1983a), where the
ankle was more dorsiflexed at footstrike and knee
flexion velocity immediately following heel strike
was increased in harder shoes compared with softer
shoes. The interaction between the shoe materials,
shoe design, and the human runner make it difficult
to predict how an individual may react to a given
shoe (Frederick 1986). This may also explain why
it has been difficult to make direct connections
between footwear, impact forces and injuries. Since
runners may alter their running mechanics in subtle
ways, depending on the shock absorption and
stability features in shoes, this may make it more
difficult to identify how differences between shoes
affect force magnitudes, movement and, indirectly,
injury.
Concluding comments
The dynamics of running involve a complex interaction between physiological and mechanical mechanisms. Our understanding of why runners adopt
specific movement patterns will mature faster the
more we analyse running from a multidisciplinary
perspective. A runner is constantly processing a
variety of different types of information from both
external and internal sources that relate to both the
movements involved and the consequences of those
movements. Scientists need to process the same
diversity of information. Many of the commonly
described relationships discussed in the preceding pages between biomechanical parameters and
either metabolic energy cost or musculoskeletal
injury are still without strong scientific confirmation. Still relatively little is known about the precise mechanisms relating how running movements
affect energy consumption or tissue stress, and
future efforts should be directed towards identifying such mechanisms. At the same time, much has
been learned in the past two decades, and there
has been an encouraging trend to more sophisticated studies that go beyond describing ‘what’ and
explores in more detail ‘how’ and ‘why’.
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Chapter 9
Resistive Forces in Swimming
A.R. VORONTSOV AND V.A. RUMYANTSEV
The nature of hydrodynamic resistance
and its components
The body of a swimmer moving through the water
experiences a retarding force known as resistance
or drag. The nature of hydrodynamic resistance is
explained by such physical properties of water as
internal pressure, density (responsible for hydrostatic force) and viscosity. While travelling through
the water the body will displace some water from its
path. The reaction of the water to the moving body
appears as: (i) pressure forces perpendicular to its
frontal area; and (ii) friction forces acting along the
body surface. Since swimming occurs in the state
of ‘hydrostatic weightlessness’ the major part of
mechanical work a swimmer performs is directed to
overcoming the hydrodynamic resistance. One of
the most obvious manifestations of this force is the
slowing-down while gliding and then stopping that
a swimmer experiences soon after a dive or pushoff.
A better understanding of how the swimmer’s body
interacts with water flow and how hydrodynamic
resistance may be reduced using appropriate swimming skills within the framework of the swimming
rules should help to increase the swimmer’s velocity
and maximize swimming achievements.
Hydrodynamic resistance (HDR) may be divided
into two categories:
• passive resistance (or passive drag) is that experienced by a swimmer’s body during passive towing,
during exposure to water flow in a water flume, and
when performing gliding without movements; and
• active resistance (or active drag) is that experienced
by a swimmer during swimming. It incorporates
184
passive resistance of the core body and additional
wave-making and eddies caused by swimming
movements (Clarys 1978; Kolmogorov & Duplisheva
1992).
Actually, both active and passive resistance
to a swimmer’s forward motion have several
components:
1 resistance by the air to above-water parts of the
body and recovering arms (only while swimming or
towing on water surface);
2 friction between water and the surface of the
body; and
3 pressure resistance, which includes:
(a) form resistance caused by eddy formation in
the body’s wake and behind its segments; and
(b) wave-making resistance.
The aerodynamic resistance is very small and
contributes little to total resistance during swimming since maximum swimming speeds are low
compared with locomotion on land, or to rowing,
and only relatively little of the body is exposed to
the air. Thus, the prime attention of coaches and
swimmers should be focused on frictional, wavemaking and pressure components of hydrodynamic
resistance.
Passive hydrodynamic resistance
(passive drag)
Swimmers experience passive drag only during the
glide after the start and turns and also possibly during some transitional postures within movement
cycles (especially in breaststroke and butterfly).
Knowledge of the components constituting passive
resistive forces in swimming
hydrodynamic resistance and their interaction with
the swimmer’s body at different flow velocities and
body alignments is basic for the development of a
proper swimming technique. That is why passive
hydrodynamic resistance is one of the favourite
research topics in sport swimming.
The magnitude of the passive hydrodynamic
resistance (passive drag) may be established experimentally by towing a swimmer in a towing tank
or exposing the subject to water flow in a swimming
flume. It is described by the formula:
FDP = 1/2 CDP ρV 2 SM
(9.1)
where ρ = water density, V = speed of the water flow
interacting with the body, SM = the area of middle
section, and CDP = hydrodynamic coefficient or
drag coefficient—a dimensionless quantity which is
defined as the ratio FDP/[(ρV2/2)SM]. The drag
coefficient is a function of another dimensionless
quantity known as the Reynolds number:
Re = ρVL/µ
(9.2)
where ρ = water density, V = flow velocity (towing or
gliding speed), L = body length, and µ = coefficient
of dynamic viscosity (µ = 0.987 × 10 –3 N · s · m –2 at
water temp. = 26°C).
Reynolds number (Re) in fluid mechanics is a criterion of whether the flow is perfectly steady and
streamlined (i.e. laminar flow), or is on average
steady with small fluctuations, or is turbulent. The
character of water flow around a swimmer’s body
(i.e. whether it is laminar or turbulent) determines
the magnitude of hydrodynamic resistance.
Laminar or streamlined flow is flow in which the
water travels smoothly and rectilinearly, without
any disturbances. The velocity and pressure at each
point of such flow remain constant. Laminar flow
may be depicted as consisting of thin horizontal
layers or laminae, all parallel to each other. Laminar
flow usually occurs when a body has a streamlined
profile and its velocity is low. With increased flow
velocity, perturbations and eddy formation occur,
until the flow pattern is so disturbed that the flow
becomes turbulent.
Turbulence also arises within boundary layers
around solid objects moving through steady water
when the rate of friction within the boundary layer
185
becomes large enough. It occurs during both active
swimming and passive towing. The boundary layer
is a thin layer of liquid in contact with the body surface. The fluid in a boundary layer is subject to friction forces, and a range of velocities exists across the
boundary layer, from maximum to zero. Boundary
layers are thinner at the leading edge of the body
and thicker towards the trailing edge. The flow in
such boundary layers is generally laminar at the
leading or upstream portion of the body and turbulent in the trailing or downstream portion.
According to Clarys (1979) for competitive swimming the Reynolds number (Re) is within the range
2 × 105–2.5 × 106. At this high Re, the inertial forces
dominate, which means that the boundary layer
along the rigid body is expected to be turbulent. In
contrast to laminar flow the resistance in such flow
is increased considerably. A number of experiments with rigid bodies of different shapes over a
wide range of Re values have shown that the drag
coefficient (CD) is a function of Re. From appropriate
diagrams CD can be estimated on the basis of Re and
incorporated into Eqn. 9.2.
Frictional resistance
Frictional resistance (or skin resistance or skin drag) is
originated in boundary layers. During swimming
the water layer in contact with the body surface
‘sticks’ to it and travels with the same speed as the
swimmer. Due to water viscosity this layer interacts with the adjoining external layer and drags
it along with it, albeit at a rate slightly slower than
the proximal boundary layer (and so on across all
components of the boundary layer). The greater the
amount of water a swimmer trails behind him, the
greater is the frictional resistance.
Smoothness of body surface, skin, hair, and tightness of the swimsuit and nature of its fabric are
the main contributors to friction resistance since
they increase the formation of eddies in the boundary layer. An increase of turbulence in the boundary layer is accompanied by increased resistance.
To form eddies the water molecules take away
kinetic energy from the swimmer’s body. Thus friction slows down swimming velocity and increases
energy losses.
186
locomotion
Frictional resistance may be estimated as:
Ffr = µ(dV/dZ)Sfr
(9.3)
where µ = coefficient of dynamic viscosity (µ = 0.897
× 10 –3 N · s · m–2 at t = 26°C), dV = difference
between velocity of water layers (dV = V), dZ =
difference in thickness of water layers, and Sfr =
wetted body surface area.
Though frictional resistance is considered mainly
as a part of passive resistance, it definitely reduces
the swimmer’s speed during gliding and in some
phases of swimming where water flow along the
body is laminar. During active swimming at high
velocities the formation of eddies in boundary
layers diverts some of the body’s propulsive energy
and thus reduces the efficiency of the swimming
technique. That is why smooth body surfaces (skin
shaving) and specially designed swimsuits help to
reduce the body’s surface-to-water friction. These
are considered to be important measures for improving swimming performance. High buoyancy
reduces the wetted body area and thereby assists in
the reduction of friction.
It is still debated whether skin shaving really
reduces turbulence in the boundary layer and
thereby reduces the frictional resistance, or
whether psychological effects are responsible for
the improved swimming performance. Sharp and
Costill (1989) found that swimmers who shaved
their skin before a race demonstrated relatively less
energy expenditure, greater stroke distance and
faster swimming velocity than those who swam
without shaving. Such increased performance may
be the result of reduction of skin friction.
Another approach to reducing friction resistance
is the development of better designs and fabrics
for swimsuits. Modern designs incorporate waterrepelling and ultra-thin elastic fabrics to maximize
body smoothness, or use fabrics that can ‘bind’ a thin
water film as a lubricant. This is an area of intense
competition between swimwear manufacturers.
Pressure resistance (form drag)
A water flow exerts a resistance force FD on any
obstacle in its path. The same force arises when a
swimmer moves through stationary water. Accord-
ing to Bernoulli’s principle any change in kinetic
power of the water flow is accompanied by an opposite proportional change of its pressure on the body
surface:
pVi2/2 + pi = constant
(9.4)
where pVi2/2 = kinetic energy of a fluid volume and
pi = potential energy of pressure of that volume. It
follows from Eqn. 9.4. that the magnitude of pressure forces acting in a direction perpendicular to the
body surface changes with the square of the flow
velocity.
Pressure resistance is the result of hydrodynamic
processes occurring at the front and rear of the moving body. Water pressure in the wake of the body is
less then pressure acting on the front. This is due to
boundary layers moving relative to the body and
each other, thereby performing mechanical work,
which slow down and separate from the body surface before they reach the rear portion. Separating
water layers form eddies, i.e. rotating water masses
with high velocity. Thus behind the point of separation an area of low pressure is formed. The pressure
difference between the front and rear of the body—
the pressure gradient—determines the magnitude
of the pressure resistance given the largest crosssectional area (SM) perpendicular to the forward
motion of the body. Hence, pressure resistance is a
result of the pressure gradient created between the
high pressure as the swimmer’s leading surfaces are
propelled through the water, and low pressure in
the swimmer’s wake caused by eddies.
When a well-streamlined body moves at slow
velocity, the boundary layers pass smoothly over
the trailing surfaces and very little eddy formation
occurs. In this case the pressure resistance will tend
to zero and total hydrodynamic resistance will be
determined predominantly by friction force. As the
swimming velocity increases and the boundary
layer around the body decreases in thickness, the
effect of the skin friction becomes less and less
important compared with the effect of the growing
pressure gradient. Eddy formation increases and
the point of the boundary layers’ separation shifts
closer to the front of the body. At near maximal
swimming velocities it appears as if a swimmer is
surrounded by a ‘cloud’ of eddies.
resistive forces in swimming
187
Table 9.1 Reynolds numbers and coefficients of form resistance for different body profiles. (After Clarys 1978.)
Body profile
Reynolds number
(Re) (= VL/ν*)
Coefficient of form
resistance (CD)
Form of the droplet
104–106
0.05
Dolphin
7.5 × 104 –7.0 × 107
0.05–0.08
Human body
6.6 × 105 –3.5 × 10 6
0.58–1.04
* ν = µ/ρ
The pressure resistance force changes as:
FP = CD(ρV2/2)SM
(9.5)
where SM is the maximal cross-sectional area of the
body interacting with the water flow, and CD is the
dimensionless coefficient of resistance.
Experimental
studies
(Karpovich
1933;
Onoprienko 1968; Clarys 1978) showed that the
form (the profile of the longitudinal section) of the
body has the greatest impact upon pressure resistance. The impact of body form finds its manifestation in the magnitude of CD. Therefore, the pressure
resistance is also denoted as form resistance, and CD
as the coefficient of form resistance.
Fast-swimming fishes and sea mammals (e.g. dolphins) have a well-streamlined form (longitudinal
contour) of the body. The body of a human with the
same length-to-width ratio as a dolphin experiences much greater hydrodynamic resistance at the
same speed. The reason is the existence of a large
number of local pressure resistance centres—the head,
shoulders, buttocks, knees, heels, etc. Clarys
(1978) reported significant differences in CD values
for bodies with relatively equal length and crosssectional area, but different hydrodynamic profiles
(Table 9.1).
As form resistance increases with the square of
the swimming velocity, its importance in competitive swimming is greater than skin friction, which
increases linearly with swimming velocity. It
follows from Eqn. 9.5 that the factors affecting the
magnitude of form resistance during swimming
at the same velocity are shape (CD) and frontal
cross-sectional area. Form resistance also depends
upon body buoyancy: high body position relative
to the water surface leads to a reduction of the
cross-sectional area that is exposed to water flow
during swimming.
How large the form drag is and how it may be
reduced are questions of practical importance for
coaches and swimmers. Sharp edges favour the
formation of eddies, and thereby increase the drag.
Deviations of a swimmer’s body and head from a
horizontal alignment as well as body actions that
increase the angle of attack (body projection relative
to the oncoming water flow) also cause an increase
in form resistance and should be avoided. A swimmer is able to reduce form resistance by stretching
and streamlining the body, choosing an optimal
depth of leg kick, and synchronizing rotation of the
hips and shoulders. The main concern for a swimmer is to have streamlining of the body in those
phases of the swimming cycle that create maximal
propulsive force. This will significantly increase the
efficiency of pulling actions (Toussaint & Beek 1992;
Maglischo 1993).
Impact of underwater torque upon pressure
(form) resistance
Underwater torque is the result of the downward
gravitational force and the upward buoyant force
acting on the body at different points and thus
inducing a couple or torque. The gravitational force
acts through the body’s centre of mass, while the
buoyant force acts through the centre of buoyancy.
By definition the centre of buoyancy is the centroid
of the displaced volume of the water and is dependent on the distribution of the displaced volume of
the fluid relative to the body. The resulting torque
188
locomotion
Rresult
Llift
Dform drag
(a)
y
R
L
α
D
Water flow
x
(b)
will tend to align the centre of mass and centre of
pressure resulting in an upright position in the
water. During swimming this torque can influence
the hydrodynamic resistance by changing the body
orientation relative to the water flow. At zero velocity the swimmer assumes an upright position in
the water, hence CD has its maximal value. During
swimming at low and moderate velocities the swimmer’s body will adopt an inclined position. The
angle between the longitudinal body axis and the
velocity (flow) direction is called the angle of attack
and denoted as α. Since the projection of the body in
the direction of gliding/swimming increases with
angle of attack it is accompanied by an increase
of passive/active pressure resistance acting on the
swimmer. The resulting hydrodynamic force has
a normal component (lift) acting upwards at right
angles to the flow/swimming direction, and a drag
force acting in a direction opposite to the swimming
velocity (Fig. 9.1).
With increased towing/swimming velocity the
lift created by the oncoming flow raises the legs
z
Fig. 9.1 The origins of normal (lift)
and frontal (drag) components of
resultant hydrodynamic resistance
(R) due to the angle of attack (α)
induced by: (a) underwater torque
and (b) deviation of the body from
horizontal alignment. D, drag; L, lift;
R, resultant resistance; α, angle of
attack.
and lower body of the swimmer and thereby
reduces the angle of attack and hence CD (Alley
1952; Onoprienko 1968; Clarys 1979). When the
body reaches a horizontal position, the lift sharply
decreases and CD stabilizes. Experimental studies
detected three phases in CD dynamics with increase of swimming velocity: (i) reduction of CD
due to decrease of the angle of attack; (ii) phase
of stabilization; and (iii) increase of hydrodynamic coefficient CD due to increased wavemaking resistance at swimming (towing) velocities
of 1.7–1.8 m · s–1 (Alley 1952; Counsilman 1955;
Onoprienko 1968).
To estimate how the resistance increases due to
the underwater torque in the glide position usually
involves comparing two sets of measurements: one
set is made during movement of the passive body
in an artificial horizontal position, the other is made
in a natural posture. The horizontal body position
is created with the help of additional buoyancy.
Onoprienko (1968) used for this purpose a set of
small spherical floats with very small resistance,
resistive forces in swimming
189
Table 9.2 Impact of underwater torque on hydrodynamic resistance (FD) during passive towing in streamlined glide
position. (From Onoprienko 1968; adapted by Rumyantsev 1982.)
Towing velocity (m · s−1)
FD ± SD (N)
Towing without
additional leg support
Towing with additional
leg support
Difference (%)
0.85
1.1
1.45
1.9
3.98 ± 0.48
4.99 ± 0.45
7.17 ± 0.76
13.64 ± 1.0
3.16 ± 0.27
4.46 ± 0.32
6.90 ± 0.72
13.48 ± 1.0
P < 0.01
P < 0.05
attached between the lower legs of the swimmer.
Table 9.2 gives the values of resistance obtained
during a towing experiment in the glide position
on a water surface with and without additional
buoyancy. The results indicate that a high hip position
relative to the water surface is an important feature
of a rational swimming technique.
One of the distinct biomechanical characteristics
of competitive swimming strokes is the magnitude
of the angle of attack. It is minimal and relatively
constant in the front crawl, then increases progressively through the back crawl, butterfly and
breaststroke. Both the butterfly and breaststroke
are characterized by angles of attack that are permanently varying during the movement cycle. The
angle of attack in these swimming strokes may be
positive or negative (depending on whether the
shoulder girdle is above or below the hips; see
Fig. 9.2). With an increase of the angle of attack
from 0 to 5° the hydrodynamic resistance (HDR)
increases by up to 15%, while an angle of attack of
18° gives a 50% increase in HDR (Onoprienko 1968).
Although intracyclic changes of the angle of attack
are inevitable, swimmers should minimize the
amplitude of the body’s up-and-down movements
(and thus minimize the SM and CD), especially
during the main propulsive phase of the arm-pull.
This will help to increase the maximal and average
intracycle swimming velocity.
Wave-making resistance
Wave-making resistance is produced when a swimmer moves on or at a small depth under the surface.
Breaststroke
End of insweep
α°
+
Arm recovery
+ leg kick
α°
+
15
12
12
8
8
4
4
0
0
–4
–4
–
(a)
Arm pull
Butterfly
t
–8
–
End of arm recovery
T of swim cycle
(b)
End of recovery/1st kick
Arm pull
2nd kick + arm
recovery
t
Immersion
T of swim cycle
Fig. 9.2 Intra-cyclic change of the angle of attack in (a) breaststroke and (b) butterfly stroke. α, angle of attack; t, time;
T, time of swim cycle. (Bulgakova & Makarenko 1996; adapted from Haljand et al. 1986.)
190
locomotion
Part of the water displaced by the body along its trajectory moves up from a zone of high pressure to
a zone of low pressure (above the non-disturbed
water level). Thus prime wave forms. This process
is accompanied by mechanical work done by the
swimmer against gravity and against the inertia of
an amount of water lifted above the surface. The
force of wave-making resistance is proportional to
the energy, contained within the front or prime
wave generated by the body and may be calculated
as (Rumyantsev 1982):
FW = ρ(A3/λ2) (V sin α)3 cos α ∆t
(9.6)
where ρ = water density, A = amplitude of the
wave, λ = length of the wave, V = wave velocity
(= swimming or towing velocity), ∆t = time unit, and
α = angle between the direction of general centre of
mass (GCM) movement and the front of the prime
wave.
According to Eqn. 9.6, the wave-making force is
proportional to the cube of the swimming (towing)
velocity, whereas the form (pressure) resistance
increases with the square of the velocity. This means
that the relative contribution of the wave-making
resistance to the total hydrodynamic resistance becomes significant at near-maximal swimming velocities (Alley 1952; Gordon 1968; Onoprienko 1968)
and may be an essential factor limiting increases in
swimming speeds.
Two wave patterns are formed:
1 divergent waves, namely the ‘stern wave’ and the
‘bow wave’, which are pushed out by front and rear
parts of the body; and
2 transverse waves, which are also formed at the
front and rear portions of the body but move at
right-angles to the direction of travel.
Parts of the body such as the shoulders and buttocks also generate waves during swimming, as do
excessive horizontal and vertical movements of the
head and upper body. The waves are visible evidence
of energy losses resulting from movements of the
body, which require that water is pushed out of the
way. A characteristic feature of waves generated by
a swimmer’s body is that they travel at the same
speed as the swimmer and their crest-to-crest length
is equal to the distance covered by the swimmer per
second. As swimming velocity increases, the crestto-crest wavelength increases until the swimmer’s
waterline length is the same as the crest-to-crest
length of his wave pattern (the point when Lwave =
waterline length is called the hull speed, a term from
shipbuilding introduced into sport swimming by
Miller (1975) ). At that velocity the swimmer is
trapped in a self-created hole between crests of
waves. The more effort that is applied, the deeper
the hole and any further attempts to increase swimming speed simply make it impossible for the swimmer to ‘climb out of the hole’. It follows from
theoretical assumptions and analogies that it is
not possible to travel on the water surface faster
than 1 bodylength × s–1. Even if the arm length is
included in the waterline length, the theoretically
estimated maximal swimming velocity Vmax should
vary (due to change in body posture) between
1.9 and 2.6 m · s–1 for individuals of height 1.95 –
2.00 m, and between 1.7 and 2.3 m · s–1 for individuals of height 1.75 –1.85 m. Although unconfirmed
by research, there is an opinion among specialists,
supported by some sport statistics, that taller
swimmers have an advantage over shorter ones
in sprint events (Miller 1975; Counsilman 1977;
Toussaint et al. 1988). This suggestion is based on
the Froude number (Fn), a dimensionless criterion
of wave-making:
Fn = V/√(gL)
(9.7)
where V = swimming velocity, g = acceleration due
to gravity, and L = swimmer height.
Since low values of Fn are associated with
decreased wave-making resistance, an increase in
height should result in decreases of Fn and wavemaking resistance. Toussaint et al. (1990) showed
that in children an increase of height from 1.52 to
1.69 m during a 2.5-year longitudinal study resulted
in a decrease of Fn from 0.324 to 0.308 at a swimming velocity of 1.25 m · s–1 (Table 9.3). Since no
significant difference in HDR was found between
repeated measurements, Toussaint et al. supported
the idea that increased pressure drag, caused by a
15% increase in the subjects’ body cross-sectional
area, was compensated by a decrease in wavemaking resistance.
resistive forces in swimming
191
Table 9.3 Effect of a 2.5-year period of growth on different parameters in young swimmers (N = 13). (From Toussaint
et al. 1990.)
1985
value
±SD
1988
value
±SD
Change
in value
±SD
Significance
Anthropometry
Height (m)
Weight (kg)
Body c/sectional area, SM (m2)
1.52
40.0
0.064
0.06
6.8
0.004
1.69
54.7
0.074
0.08
7.1
0.006
0.17
14.7
0.010
0.05
5.7
0.005
P < 0.001
P < 0.001
P < 0.001
Dimensionless form indices
Length/width ratio
Length/depth ratio
Length/thickness ratio
Width/depth ratio
4.83
9.35
36.5
1.95
0.29
3.57
3.57
0.19
4.65
39.4
39.4
2.13
0.33
3.04
3.04
0.21
−0.18
2.97
2.9
0.18
0.34
3.73
3.73
0.24
NS
P < 0.05
P < 0.05
P < 0.05
Drag
FD at V = 1.25 m · s−1 (N)
30.1
2.37
30.8
4.50
0.7
3.4
NS
Non-dimensional indices
Reynolds number (V = 1.25 m · s−1)
Froude number (V = 1.25 m · s−1)
CD (V = 1.25 m · s−1)
2.2 × 10 6
0.324
0.64
0.08 × 10 6
0.007
0.069
2.5 × 10 6
0.308
0.54
0.12 × 10 6
0.006
0.077
0.25 × 10 6
−0.016
−0.089
0.07 × 10 6
3.8 × 10 −4
0.0058
P < 0.001
P < 0.001
P < 0.001
Performance data
100 m time (s)
Vmax ( m · s−1)
Fmax (N)
Pmax (W)
72.8
1.37
37.4
51.7
5.84
0.08
6.57
11.58
62.9
1.53
50.2
77.2
3.25
0.07
7.92
14.81
−9.9
0.16
12.8
25.5
3.1
0.05
5.84
9.66
P < 0.001
P < 0.001
P < 0.001
P < 0.001
The influence of depth of submersion upon
resistance
If the body moves underwater and waves do not
appear on the surface it means that the potential
energy of water layers above the body is greater or
equal to the energy of high flow pressure of water
layers which are in contact with the body. Thus
the minimal depth of gliding or swimming, when
no waves appear on water surface—the depth of wave
equilibrium—may be determined as:
hp = V2/2g × Cw
(9.8)
where V = body velocity, g = acceleration due to
gravity, and Cw = non-dimensional wave-making
coefficient. In cases where a swimmer may be
affected by waves created by his opponents, hp may
be determined as wave base level—the depth at which
wave energy can no longer affect the body:
hp = λ/2 = V/2
(9.9)
where λ = length of the wave, which is equal to the
swimming velocity. It seems that the depth at
which the wave-making resistance is negligible
lies between 0.7 and 1.2 m. When the body moves
deeper than hp body resistance does not change. If
the depth of swimming (towing) is less than hp ,
body movement through the water is accompanied
by the formation of waves, which cause an increase
in total hydrodynamic resistance. When part of the
body is above the water surface, a reduced frontal
area will create pressure resistance and friction
becomes much less, but the wave-making resistance
will sharply increase. The practical question which
arises is whether the total HDR on the surface is
greater than that during underwater swimming.
Since wave-making resistance changes with the
cube of swimming speed, it becomes a sizeable component of total HDR at maximal speed. As gliding
speed after a start and turns is much higher than the
average racing speed and waves are not produced
192
locomotion
Table 9.4 Relationship of hydrodynamic resistance measured during towing of swimmers using the same gliding
postures on and under the water surface.
Authors
Towing
connection type
Subjects (number
and sex)
Depth of
towing (m)
Towing velocity
(m · s−1)
Difference on/
under surface (%)
Schramm (1959)
Flexible
N = 2, males
0.5
1.7
10.5
Ilyin (1961)
Flexible
N = 1, male
1
1.4
1.8
6
4
Onoprienko
(1968)
Flexible
N = 1, male
0.5
1.1
1.9
13
9
Gordon (1968)
Flexible
N = 15, males
0.5
1.5
1.9
15
10
Clarys et al.
(1974)
Rigid
N = 53, males
0.5
1.5
1.9
−22
−18
* Cited by Rumyantsev (1982).
during a deep glide, it is beneficial to reach and
maintain this high gliding speed for a longer time
using a leg kick only.
Results of experimental studies on the magnitude
of hydrodynamic resistance experienced by swimmers on and under the water surface still remain
controversial because of differences in design of
towing devices and procedures (posture, depth of
towing) employed (Table 9.4). Researchers who
found resistance on the surface to be higher than
that during underwater towing used flexible connections between the swimmer and the towing
device. Such attachments provide higher stability
of the body within the water flow during towing
underwater than on the surface. This may account
for the finding of greater resistance during surface
towing than under water. Those authors who found
opposite results (Clarys et al. 1978, 1979; Clarys &
Jiskoot 1974) used towing devices with a rigid
attachment to the swimmer. Thus identical posture
and body orientation were provided for both underwater and surface towing.
Phenomenal results have been achieved by some
outstanding performers in the backstroke and butterfly disciplines (e.g. D. Berkoff, I. Poliansky, D.
Suzuki, D. Pankratov and M. Hyman), who covered
up to 50 – 60% of the competitive distance underwater using only the butterfly kick on the front, back or
side. Such performances provide strong grounds for
a re-evaluation of the ratio of hydrodynamic resistance on and under the water. Is underwater swimming really faster than swimming on the surface?
Sport practice shows that swimming underwater
using kick only is at least no slower than swimming
on the surface using the full stroke. If one accepts the
physiological data showing that the leg kick is much
less efficient than the arm pull, it is possible that due
to the absence of wave resistance the total hydrodynamic resistance during underwater swimming
at high velocity is less than during swimming on the
water surface. The record tables of fin swimming
support this point of view. The competitive programme in fin swimming includes events both on
the surface and underwater. The record times for
underwater events are significantly faster than for
surface swims (Table 9.5). One more interesting
Table 9.5 World fin swimming records in surface and
underwater events.
Surface
(only 15 m dive)
Breathhold*
or scuba
Event
Males
Females
Males
Females
50 m
100 m
400 m
800 m
16.07
36.44
3.04.58
6.34.18
18.58
40.96
3.20.37
6.59.44
14.83*
33.65
2.52.65
6.08.29
16.28*
36.26
3.01.84
6.30.14
resistive forces in swimming
fact is that nuclear submarines, using the same
engines both on and under the surface, achieve their
maximum velocity when submerged (the speed
record belongs to Russian submarines—44.5 knots
or 82.5 km · h–1). When surfaced, their maximum
speed is less than half of that when submerged!
This is despite the fact that the friction, form and
appendage resistance of submarines is much higher
under water than on the surface.
The latest Federation Internationale Natation
Amateur (FINA) rules for competitive swimming
limit the distance which swimmers are allowed to
cover under water to 15 m. However, the nature
of the resistance experienced by swimmers on and
under the surface requires further investigation
since swimmers can still travel significant distances
under water after the start and turns.
Total hydrodynamic resistance
It is commonly recognized that total hydrodynamic
resistance of the body during passive towing is
a sum of its friction, wave-making and form
components:
Ftotal = Ffriction + Fwave-making + Fform
(9.10)
The formulas and values used by Rumyantsev
(1982) to calculate total hydrodynamic resistance
for a swimmer’s body are given in Table 9.6. For a
flow velocity of 2.0 m · s–1 these components have
approximately the following magnitudes:
193
Fform = 93.5 N
Ffriction = 0.05 N
Fwave-making = 5 N
The total hydrodynamic resistance is 98.55 N.
These calculations cannot be accepted as precise,
but they help to assess the relative contribution of
friction, wave-making and form resistance to total
resistance at different towing and gliding velocities.
Thus the share of wave-making resistance may
reach its maximum at a water velocity of 2.0 m · s–1
and above. At lower velocities wave-making resistance is less significant. Calculations show that
friction resistance is less than 1–2% of pressure
resistance. Since the friction acts along the body
surface, it acts most efficiently in laminar flow;
transition to turbulent flow is accompanied by predominance of frontal drag forces over friction. The
human body is not a perfect hydrodynamic body. It
creates a big area of turbulence in the surrounding
boundary layers and in the wake at higher towing
velocities. This decreases the impact of friction
resistance upon total HDR. Nevertheless, some
authors still support a prevailing role of friction in
total body resistance during swimming. As a rule
such conclusions are made on the grounds of results
of correlation analysis between total hydrodynamic
resistance and body surface area (Karpovich 1933;
Onoprienko 1967a, 1968). The fact that the overwhelming majority of studies found a seconddegree relationship between swimming (towing)
velocity and total hydrodynamic resistance lends
Table 9.6 Formulas and values (ranges) of variables for calculation of contribution of different kinds of resistance into
total resistance. (From Rumyantsev 1982.)
Pressure (form) resistance (Fp )
Friction resistance (Ffr )
Wave-making resistance (Fw)
Fp = CxρV2SM/2
Ffr = µSfr(dV/dZ)
Fw = ρA3/λ2 (V sin α)3 cos α
CDP = 0.85 (0.5–1.20)
SM = 0.055 m2 (0.91– 0.1 m2)
ρ = 1000 kg · m−3
V = 2 m · s−1
µ = 1 × 10−3 N · s · m−1
A = 0.75 m (0.05–0.1 m)
λ = 4A (3–5A)
α = 32.5° (20–45°)
V = 2.0 m · s−1
ρ = 1000 m3
Sfr = 1.75 m2 (1–2.5 m2)
dV = V = 2 m · s−1
dZ = 0.55 m (0.01–0.1m)
A = amplitude of wave; CDP = drag coefficient; dV = difference between velocity of water layers; dZ = difference in
thickness of water layers; Sfr = wetted body surface area; SM = maximal cross-sectional area of body; V = velocity;
α = angle between direction of GCM movement and front of prime wave; λ = length of wave; µ = coefficient of dynamic
viscosity; ρ = water density.
194
locomotion
support to the predominant role of form (pressure)
resistance in swimming. If frictional resistance
were predominant, a linear relationship would be
expected. Miyashita and Tsunoda (1978) found that
the total hydrodynamic resistance of well-trained
swimmers is much less than that of novice swimmers despite the fact that the latter had as much as a
two times smaller body surface area. It is likely that
experienced swimmers may assume a more streamlined position in the water and thus reduce crosssectional area and form resistance. (Since the data
were obtained in a water flume it seems possible
that skilled swimmers can control and reduce
the turbulence in the body’s wake and pressure
gradient by minor leg movements.) In this case
an increase of frictional resistance due to a greater
surface area does not play a significant role, while
a decrease in pressure (frontal) resistance by streamlining of the body causes reduction of total HDR.
The better streamlining is attributed to longer bodies since the point of boundary layer separation is
closer to the rear thereby creating less eddy formation than with shorter bodies.
Studies on the influence of body posture and
orientation in relation to flow on the magnitude of
HDR provide evidence that the form resistance is a
major component of total hydrodynamic resistance.
It has been shown experimentally (Counsilman
FD =100%
FD =121.5%
1955; Schramm 1959; Onoprienko 1968; Chernyaev
& Maltsan 1974) that the most streamlined posture
is the gliding posture in which the body and legs
are outstretched, the toes are pointed, the arms are
stretched over the head and hands topping one
another, and the ears are pressed by the shoulders.
Thus the head is efficiently streamlined by the arms
to receive the oncoming water flow. Even minor
deviations of the head, arms and legs from a streamlined position during the glide after starts and turns
may result in a considerable increase of resistance
(Fig. 9.3).
Hydrodynamic resistance during towing on the
side or back in a glide position seems to be higher
compared with the front glide position (Counsilman 1955—for towing velocity 0.6–2.2 m · s–1; Clarys
& Jiskoot 1974—for V = 1.9 m · s–1). These results
support the opinion that body form (not body
surface area) is a decisive factor in determining the
magnitude of the total resistance.
The resistance force changes due to deviation
from a streamlined posture and horizontal alignment. Thus an increase of the angle of attack due to
a backward bending in the waist or lifting of the
head leads to an increase in resistance of 26, 20
and 12% at V = 1.1, 1.45 and 1.9 m · s–1 respectively
(Onoprienko 1968). At higher velocities the impact
of body flexion upon resistance is reduced. As a
FD =107%
FD =112.5%
Fig. 9.3 Impact of body form upon
hydrodynamic resistance during
underwater towing (the magnitude
of total resistance in glide position
conditionally accepted as 100%).
(Adapted from Bulgakova &
Makarenko 1996.)
resistive forces in swimming
Table 9.7 The impact of body posture on passive drag
during towing. (From Onoprienko 1968; Makarenko
1996.)
Posture
% Difference in total
HDR compared to
streamlined glide
position
Arms trailing along the body
+37 (V = 1.1–1.45 m · s−1)
+28 (V = 1.9 m · s−1)
Arms stretched forwards with
hands at shoulder width
+7.7 (V = 1.1–1.8 m · s−1)
+9.5 (V = 1.9 m · s−1)
Feet at shoulder width,
flexed at α = 90°
+26 (V = 1.9 m · s−1)
One arm along the body,
the other stretched forwards
+12.5 (V = 2.0 m · s−1)
result of the greater lift the body is moved to a
higher position relative to the water surface and this
tends to counteract the increased resistance. During
active swimming a relatively high head position to
facilitate breathing should be maintained. It was
found that even minor deviations of the head position from a horizontal alignment at flow velocities
in the range 1.7–2 m · s–1 caused increases of total
HDR from 2 to 7% up to 30–40% (Onoprienko 1968;
Miyashita & Tsunoda 1978). Table 9.7 demonstrates
the impact of swimmer posture upon total HDR
(Onoprienko 1968; Chernyaev & Maltsan 1974;
Rumyantsev 1982; Makarenko 1996). Analysis of
the influence of body build and composition
upon hydrodynamic resistance revealed that the
most informative characteristics of passive drag
are the area of maximal cross-section of the body,
and the circumferences of the head and shoulders
(Table 9.7). This again emphasizes the importance of
pressure resistance in swimming. As a rule crosssectional dimensions demonstrate a higher correlation with passive resistance than longitudinal ones.
A positive and significant correlation between
passive resistance and body weight and volume has
been found by Clarys (1978) and others. These characteristics correlate closely with cross-sectional area
(r = 0.9). Some authors found significant correlation
between body surface area and resistance (Clarys
et al. 1974), while others (Miyashita & Tsunoda 1978)
195
found no correlation between passive resistance
and any anthropometric variable.
In shipbuilding, proportional indexes are widely
used to characterize the hydrodynamic qualities of
the hull. Numerous attempts have been made to find
anthropometric substitutes for hull indexes. Clarys
(1978), Miyashita and Tsunoda (1978), Onoprienko
(1968) and Safarian (1968) studied the relationship
between passive drag and anthropometric indexes
of proportionality. They found very few significant
(P < 0.05) correlation coefficients between total
HDR and proportions of the human body. All these
authors concluded that anthropometric indexes are
useless for characterizing the hydrodynamic qualities of the human body (Table 9.8). In comparison
with the relatively smooth ship contours, the human
body has a great number of local pressure points.
The bony hillocks raised over the surface of the
human body (such as knee joints and heel bones)
cause increased eddies and thus increase the resistance during swimming. This may distort the
influence of body proportions upon total HDR. Skin
fat may have some positive impact on hydrodynamic qualities of the human body since it improves
buoyancy and smoothness of the body profile. It is
presumed that human skin and the subcutaneous
fat layer reduce turbulence of the boundary layers
and thus decrease resistance. An experiment in
which a rigid life-size human body model and a
female swimmer with well-developed subcutaneous fat were towed revealed no difference in HDR
at a velocity of 1.5 m · s–1. However, at a towing
velocity of 1.9 m · s–1 the swimmer had 6% less resistance than her own body’s model (Onoprienko
1968). Actually, the differences in thickness of skin
fat among top swimmers may be too small for this
factor to assume significance in reducing the total
hydrodynamic force during swimming. It is well
known that the swimsuit should be manufactured
from smooth, thin, waterproof fabric that tightly fits
the body surface. Schramm (1959) found that the
resistance of a swimmer wearing a swimsuit two
sizes too big increased significantly during towing
(V = 1.7 m · s–1). Onoprienko (1968) found resistance
increased by 3% (V = 2.0 m · s–1) during towing of
a female swimmer wearing a woollen swimsuit
compared with a silk swimsuit (in addition to the
196
locomotion
Table 9.8 Correlation of anthropometric characteristics and hydrodynamic resistance.
Miyashita &
Tsunoda (1978)
Author
Clarys (1978)
Safarian (1968)
Onoprienko (1968)
Method of
towing
Electromechanical
with mobile
carriage
Electromechanical
with stationary
platform
Electromechanical
with stationary
platform
Water flume
Subjects’ details
N = 44 males
Height = 180.9
(± 6.4) cm
mg = 73.8 ± 7.3
N = 77 males
Height = 176.7
(± 6.2) cm
mg = 70.8 ± 8.1
N = 92 males
N = 67 females
N = 8 females
Height = 153.7 cm
Posture
Front glide
Front glide
Front glide
Front glide
Towing velocity
(m · s−1)
1.5 –2.0
1.8
1.9
0.8–1.6
Chest
circumference
P < 0.05
r = 0.48 – 0.60
P < 0.05
r = 0.84
–
–
Body surface area
–
–
P < 0.05
P < 0.05
Weight
P < 0.05
P < 0.05
0.85
–
–
P < 0.05
0.57
Height
–
P < 0.05
0.62
–
P < 0.05
0.53
Body volume
P < 0.05
–
–
–
mg = 46.3 ± 10
mg = body weight.
greater frictional resistance, a woollen swimsuit
trails a large mass of water behind the swimmer).
Evaluation of passive resistance
It is extremely difficult to determine the frictional,
wave-making and/or eddy resistance because the
swimmer’s propulsion along the water surface is
regarded as a collection of numerous travelling
pressure points (Miyashita & Tsunoda 1978). Therefore, researchers usually measure the resultant total
water resistance of the swimmer in relation to
velocity.
The evaluation of passive hydrodynamic resistance is based upon measurements made during
towing, or by exposing a fixed body to a water flow.
The following conditions must be fulfilled during
such experiments.
1 During towing the swimmer should remain in a
steady, immobile posture. Even minor changes in
posture or in orientation towards water flow may
cause significant changes in resistance; the type of
towing connection (rigid or flexible connection) has a
big impact on the stability of body posture (Table 9.4).
2 The towing force should act parallel to water
surface.
3 The towing device should provide uniform velocity throughout the course of towing.
During acceleration and deceleration the gauge
will record the inertia of the swimmer’s mass as well
as the resistance.
Towing devices of the inertial type, where the
potential energy of a falling body of fixed weight
converts into a towing force, do not provide a constant uniform velocity of towing. The most reliable
and precise method of measuring passive drag is by
using an electromechanical towing device. This consists of an electric motor of varying power which
is used with precise control systems to create the
necessary uniform towing velocity. The stationary
resistive forces in swimming
platform in a water tank and a mobile carriage are
used for such experiments.
During measurement of hydrodynamic resistance
in a swimming flume the swimmer’s body is
exposed to an artificial oncoming water flow created
by a propeller (Holmer 1974; Miyashita & Tsunoda
1978; Gordon et al. 1985). The swimmer is connected
to the gauge (on the deck) by a cable. The method is
very simple and permits the posture of swimmer
to be observed. The absolute values of resistance
obtained using this method are slightly lower than
values obtained during towing in water tanks. This
is due to the effect of lift on the swimmer’s body at
high flow velocities.
Since different methods and subjects are used in
different studies a great variety of data on hydrodynamic resistance is found in the references. Of more
practical value may be relative characteristics, i.e.
change of resistance with the change of flow velocity, and comparison of resistance magnitudes in
the same studies but using different body positions.
Active hydrodynamic resistance
(active drag)
If passive drag is the amount of resistance that a
human body experiences during towing through
stationary water or exposure to mobile water flow
in a water tank, in an unchanging posture, the active
drag is that associated with swimming motions.
While passive drag certainly depends upon body
size and shape, active drag has been regarded as a
function of the movements as well as a function of
the anthropometry and mechanical properties of
a rigid core body. Experimental studies based on
different measuring techniques are in accord that
the relationship between active drag and swimming
velocity is quadratical (Di Prampero et al. 1974;
Clarys 1979; Toussaint et al. 1988; Kolmogorov &
Duplisheva 1992). This means that the pressure
component is the main contributor to active resistance during swimming. The magnitude of active
resistance may be established as:
FDA = KV2 or
FDA = 1/2 CDAρV2A
(9.11)
197
where CDA is the coefficient of active drag and A is
an anthropometric variable.
Research still leaves open the nature of the
relation between active drag and anthropometric
characteristics. Clarys (1979) examined the drag
of self-propelling bodies and found significantly
higher values than those recorded for passively
towed bodies. He concluded that neither body
shape nor its composition nor skin surface area
influences the active drag. It may be considered a
product of systematic changes in shape and size
(i.e. swimming technique) and is determined by
the nature of water flow around the body.
More recently, Huijing et al. (1988) found a high
correlation between active drag and maximal body
cross-section area (r = 0.87). Toussaint et al. (1988)
also related the difference in active drag between
male (FDA = 30V2) and female (FDA = 24V2) swimmers to a larger body cross-section in males (0.091
m2 vs. 0.075 m2). The greatest difference in active
drag between males and females was found for a
swimming velocity of 1.0 m · s–1. It reduced sharply
with increased swimming velocity. Thus the contribution of anthropometric characteristics (and,
hence, the contribution of passive drag) to active
resistance decreases at high swimming velocities.
In a 2.5-year longitudinal study of active drag in
age group swimmers Toussaint et al. (1990) did not
find any increase of active drag despite marked
increases in body cross-sectional area and skin
surface. Although it had been presumed that an
increase of both parameters would be accompanied
by increases in pressure (form), friction and total
resistance, this did not happen.
The most interesting scientific fact is that no correlation has been found between the magnitudes of
active and passive drag (Clarys 1978; Kolmogorov
& Duplisheva 1992). Moreover, Toussaint et al.
(1988) and Kolmogorov et al. (1997) found the magnitudes of active drag to be 2–3 times smaller than
values reported by other authors, who used nondirect measurements. Also, their values were much
lower than could be expected if the active drag
represents a simple sum of passive drag components and additional wave-making and turbulence
resistance caused by a swimmer’s movements. In
198
locomotion
separate individual cases no significant difference
between the magnitudes of passive and active drag
was detected despite obvious differences in water
flow turbulence. Elite swimmers demonstrated a
much smaller active drag than average swimmers
over the range of swimming velocities.
Measurement of active drag
direct methods
Early measurements of active drag (AD) involved
indirect calculations based upon changes in oxygen
consumption with additional drag loaded onto the
swimmer (Di Prampero et al. 1974; Clarys 1979).
AD found in these studies was much higher than
passive drag (PD).
More recently, methods for the direct measurement of active drag have been introduced,
namely the ‘Measuring Active Drag system’ (MAD;
Toussaint et al. 1988) and the velocity perturbation
method (Kolmogorov & Duplisheva 1992). Both the
MAD system and velocity perturbation method
show that the better technique of elite swimmers
gives them much less AD than average swimmers
over a range of swimming velocities. Thus the
reduction of AD should become a target for stroke
development in swimming.
Measuring active drag (MAD) system
(Toussaint et al. 1988, 1990)
The MAD system is based on measuring the mean
propulsive force in a swimming-like activity (this system allows measurement of propulsive force during
front crawl swimming only). The swimmer pushes
off against grips, which are attached to a tube
located 0.8 m under the water surface (Fig. 9.4). The
tube is fixed to a force transducer. Thus the force a
swimmer applies during pushoff is registered. Since
at constant swimming velocity the measured mean
propulsive force, FP, equals the mean active drag
force, FDA, this method provides the mean active
drag on the swimmer. The authors found that the
mean propulsive force (using arm pull only) at a
swimming velocity of 1.48 m · s–1 appeared to be
53.2 ± 5.8 N, which is 2–3 times smaller than values
of active drag reported by other authors. It is, however, in agreement with values reported for passive
drag on a towed swimmer.
It was found that FDA in a velocity range of 1.0 –1.8
m · s–1 is related to the swimming velocity, V, raised
to the power 2.12 ± 0.20 in males and 2.28 ± 0.35 in
females.
The greatest differences in drag force and
coefficient of drag between males and females
were found for a swimming velocity of 1.0 m · s–1:
Pump
Crawl direction
A
C
B
Fig. 9.4 The measuring active drag (MAD) system: general view. (From Hollander et al. 1986.)
resistive forces in swimming
drag, 28.9 ± 5.1 N and 20.4 ± 1.9 N; drag coefficient,
0.64 ± 0.09 and 0.54 ± 0.07, respectively. These differences become less at higher swimming velocities.
Velocity perturbation method
The velocity perturbation method involves changing the maximal swimming velocity using added
drag provided by a hydrodynamic body of known
resistance towed by the swimmer (Fig. 9.5).
Swimmers performed two maximal-velocity swims
of 30 m with and without the hydrodynamic body
(HB). The HB was placed at such a distance behind
the swimmer that the water was no longer turbu-
lent. This critical distance proved to be 3.5 – 4.5 L
(see Fig. 9.5).
Swimming speed, V, and resistance force, F, were
measured during both swims. The assumption has
been made by authors that the power output (Pto1)
during swimming without the HB is equal to the
power output delivered when swimming with
the HB (Pto2): hence, Pto1 = Pto2. However, not all
power generated in swimming can be used to overcome drag. Part of it will be transferred in the form
of a flow kinetic energy (Pk). Hence, the equations
below are approximations (Toussaint et al. 1990).
According to Kolmogorov & Duplisheva (1992) the
observed difference in velocity (V2 vs. V1) should be
1
2
4
5
3
6
(a)
3.5–4.5 L
Fig. 9.5 The velocity perturbation
method. (a) The structure of the
additional hydrodynamic body:
1, carrying body (made of foamplast);
2, water line; 3, a hole for water;
4, kniveposts; 5, fixing hook for ropes;
6, hydrodynamic cylinder (made of
light metal). (b) The attachment of
an additional hydrodynamic body
(‘B’ and ‘C’) to the swimmer’s body.
L, body length. (Reprinted from
Kolmogorov & Duplisheva (1992),
pp. 311–318, with permission from
Elsevier Science.)
‘B’
‘C’
(b)
199
L
200
locomotion
due to the effect of the added resistance. Hence, in
the free swimming conditions power output during
free swimming (non-resisted), Pto1 = Fr1V1 and in
the added resistance conditions power output during swimming with hydrodynamic body attached
to swimmer, Pto2 = Fr2V2, where Fr1 and Fr2 are
active drag values. Since
Fr1 = 1/2 CDρSV12 and
Fr2 = 1/2 CDρSV22 + Fb
and since Pto1 = Pto2, Fr1V1 = Fr2V2, so it follows that:
The results were in agreement with the ideas of
Clarys (1979) and Toussaint et al. (1988) that stroke
technique is more important in reducing AD than
body composition.
In passive towing CDP depends upon the shape of
the swimmer’s body and features of the skin and
hair. In active swimming CDA quantitatively reflects
the interaction of different parts of the moving body
with the ‘passive’ flow of fluid. With the increase in
V there is an increase of turbulence in water flow
passing the swimmer’s body that facilitates the
increase in CDA.
/2 CDρSV13 = 1/2 CDρSV23 + Fb and
1
CD = FbV2/1/2 ρS(V13 – V23)
indirect methods of active drag
measurements
Substitution of CD in this equation gives:
Fr1 = FbV2V12/V13 – V23.
Since Fb is known the assessment of the magnitude
of active drag becomes a very simple procedure
of speed measurement during unloaded and loaded
swims.
The Kolmogorov–Duplisheva method allows the
measurement of active drag during swimming
using all four competitive strokes, while the MAD
system and indirect methods are applicable only to
the front crawl. The estimated error of the method is
no higher than 6 – 8%.
Kolmogorov and Duplisheva made the following
conclusions.
1 CDA and CDP do not correlate with each other.
2 A comparison of CDA between male and female
revealed no statistically significant differences.
3 Swimming strokes were ranked in terms of resistance (from low to high): freestyle < backstroke (BK)
and butterfly (Fly) < breaststroke (BR).
4 Young swimmers have a lower AD than adults.
5 The magnitudes of FDA for men’s freestyle were
much lower than those predicted previously via
indirect methods (Di Prampero 1974; Issurin 1977;
Clarys 1979:) or obtained in studies using the MAD
system (Toussaint et al. 1988, 1992).
6 Elite swimmers display a biomechanically
efficient swimming technique that is characterized
by low FDA at maximum V.
Bioenergetic methods
These methods are based on re-evaluation of the
relationship between the magnitude of towing
velocity, additional force and relevant metabolic
changes (Di Prampero et al. 1974). During active
swimming known horizontal forces are applied to
the swimmer by a towing device. The swimmer thus
has to generate additional propulsive forces, since
the total propulsive force equals the algebraic difference of his own body drag and the known force
applied to his body. It is assumed that the concomitant mechanical power (force × velocity) the swimmer has to expend is reflected in the variations of
the oxygen intake (VO2), which can be measured,
and that extrapolation of the linear relationship of
active drag and VO2 can be used to estimate active
body drag. The swimmer is connected to the towing device and performs 5 – 6 stages of continuous
swimming at constant velocity. The design of the
towing device allows an additional towing force to
be applied along the swimming direction (unloading) as well as in the opposite direction (loading).
Each swim is performed in a given time, necessary
to establish functional characteristics in a steady state.
The theoretical line of regression is constructed,
based on the experimental data, and processed
using the method of least squares. The regression
line is extrapolated towards the relative ‘zero’ of the
physiological parameter. The value of additional
resistive forces in swimming
f (VO2 l·min–1)
201
Theoretical regression line
Experimentally obtained data
Change of functional
parameter relative to
‘unloaded level’
F0 Active resistance at given
swimming velocity
F = f cos α
Fig. 9.6 Extrapolation of the active
drag based on the relationship
between the change in O2 intake and
additional towing force during
swimming at constant velocity
(method of Di Prampero et al. 1974).
(Adapted from Rumyantsev 1982.)
f
Unloading
α
F0
V = constant
–3
–2
unloading (Fo) at the point of crossing with the axis
of abscissas (axis of ∆F), according to the authors of
this method (Di Prampero et al. 1974), represents the
value of the hydrodynamic resistance which the
swimmer overcomes during swimming at a given
speed (Fig. 9.6).
Non-direct bioenergetic methods have the following requirements.
1 Swimming should be performed with minimal
fluctuations of intracyclic velocity (otherwise the
swimmer will have to overcome a water resistance which is significantly higher than the one
calculated).
2 The functional criteria chosen should reflect the
total increase in energy expenditure caused by
the change in the working regimen (intensity of
swimming).
3 To provide a more precise evaluation of active
resistance, functional changes should be measured
during steady-state swimming (one of the limitations of non-direct methods is that they allow the
measurements of active drag only for the ‘aerobic’
range of swimming velocities and are inappropriate for near-maximal and maximal swimming
velocities).
A well-argued critique of the bioenergetic
methods of determining active drag is presented by
Toussaint et al. (1992). They showed that the overall
work performed by the swimmer is the sum of: (i)
–1
∆F
Loading
0
1
2
3
Additional towing force
the work to overcome drag; and (ii) the work performed to accelerate a given mass of water backwards, which is due to the fact that in swimming a
fixed pushoff point is not available. The propulsive
force is generated by pushing against the water and
is equal to the impulse (m × v) of the mass of water
pushed away. During the pushoff, the energy
(1/2mv2) is transferred from the swimmer to the
water (Toussaint & Beek 1992).
Hence, measured variations in VO2 reflect not
only the concomitant mechanical power due to the
added drag, but also the additional power that is
dissipated during the production of the kinetic
energy in the water that is pushed away. When variations in VO2 are exceptionally attributed to variations in active drag, the active drag is significantly
overestimated. Furthermore, it is questionable to
use regression equations outside the range in which
they were established (Toussaint et al. 1990).
Modelling (transitional) method
This method consists of modelling intermediate
boundary postures of the phases of swimming
motions (swimming cycle) and is based on the
evaluation of hydrodynamic coefficients (CDP) for
different postures at different towing velocities.
Then, during active swimming synchronized video
recording and recording of intracyclic velocity are
locomotion
1 Glide position
R=4.57V1.78
2 Inhalation
R=8.41V1.70
DA
Drag (N)
202
DA(+)
0
3 Finish of leg
recovery
R=9.44V 2.16
4 Leg kick—
arm recovery
R=8.91V
2.21
5 End of leg kick—
beginning of arm
pull
R=7.90V 2.40
DA(–)
D0
Vmax
Fig. 9.7 The modelling (transitional) method: the
relationship between intermediate (boundary) body
positions and momentary values of hydrodynamic
resistance during breaststroke swimming. R = magnitudes
of resistance calculated for distinct boundary postures.
(Data from Kent & Atha 1975.)
performed. The values of the swimming velocity for
selected boundary postures are estimated. When
the duration and CDP of every phase of the swimming cycle are established, it is possible to calculate
the active resistance for a complete swimming cycle
(Kent & Atha 1975). The accuracy of this method
will depend upon the number of selected boundary
postures (Fig. 9.7), but in any case, the resulting
magnitude of the hydrodynamic force will differ
significantly from its real value. One of the reasons
is that when the body moves with acceleration, the
real active drag it experiences differs from the
values established for uniform swimming velocities. This difference is a result of the inertial force of
the added mass of the water acting on the body dur-
Velocity (m · s–1)
Fig. 9.8 Determination of active drag by extrapolation of
the drag (DA(+)) and added propulsion (DA(–)). (Reprinted
from Clarys et al. (1985), pp. 11–24, with permission from
Elsevier Science.)
ing acceleration. In order to overcome this inertia
the swimmer has to expend a significant quantity of
energy. In accordance with Newton’s Second Law,
the full hydrodynamic resistance experienced by
the body when it moves with acceleration may be
subdivided into two forces:
FDA = FDP + ∆m a
(9.12)
where FD = full hydrodynamic resistance, FDP =
resistance created by the interaction of the body
with oncoming water flow (passive resistance),
∆m = added mass of the water, a = acceleration, and
hence ma = inertia force of the added water mass.
The added mass of the water is determined by the
formula:
Ft – FDP = (m + ∆m)a
(9.13)
where Ft = towing force, m = body mass of the
swimmer, and ∆m = added mass of water. Issurin
(1977) determined the influence of intracyclic
velocity fluctuations and the inertia forces of body
mass and added water mass, (m + ∆m)a, on hydrodynamic resistance. He calculated instantaneous
values of active resistance and average resistance
for half of the cycle (for a front crawl) and found that
the values of resistance were 1.5 –2 times greater
resistive forces in swimming
than during passive towing at the same average
swimming velocity. This method certainly overestimates the value of the active drag since the
calculation includes the entire magnitude of the
passive resistance.
Method of active drag measurement during towed
swimming with constant velocity
Clarys et al. (1979) used a relatively simple method
of measurement of active drag. The swimmer
was towed with uniform velocity while performing
front crawl swimming movements. The gauge
recorded both negative force, DA(–) (due to propulsive force), and positive towing force, DA(+) (the
203
added drag). The recording was made throughout a
range of swimming speeds including the maximal
velocity of active swimming. On the graph depicting the relationship ‘towing velocity’ vs. ‘additional
towing force’ the experimental regression line was
extrapolated to ‘zero velocity’ (Fig. 9.8). The value of
the additional towing force at the x = 0 point (at zero
velocity) added to the original regression line of
additional towing force represents the active drag
force during swimming at all velocities. The active drag magnitudes obtained with the use of this
method are much higher than the magnitude of
passive drag in a gliding position and significantly
higher than active drag values obtained with the use
of direct measurements.
References
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resistance and propulsion in swimming
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Bulgakova, N.Zh. & Makarenko, L.P. (eds)
(1996) Sport Swimming. Physical Culture,
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Academy of Physical Education),
Moscow.
Chernyaev, E.G. & Maltsan, K. (1974) The
investigation of several aspects of front
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Clarys, J.P. (1978) Relationship of human
body form to passive and active hydrodynamic drag. In: Biomechanics VI-B
(eds E. Asmussen & K. Jorgensen),
pp. 120–125. University Park Press,
Baltimore.
Clarys, J.P. (1979) Human morphology
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(eds J. Terauds & E.W. Bedingfield),
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Clarys, J.P. (1985) Hydrodynamics and
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Clarys, J.P., Jiskoot, J., Rijken, H. &
Brouwer, P.J. (1974) Total resistance in
water and its relationship to body form.
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Morehouse), pp. 187–196. University
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Quarterly 26 (2), 127–139.
Di Prampero, P.E., Pendergast, D.R.,
Wilson, C.W. & Renny, D.W. (1974)
Energetics of swimming in man. Journal
of Applied Physiology 37, 1–5.
Gordon, S.M. (1968) Swimming technique
(ed. N.A. Butovich). Fizkultura i Sport,
Moscow.
Gordon, S., Dmitriev, D. & Chebotareva,
I.V. (1985) Dependency of coefficient
of resistance on low velocity, age and
anthropometric indicators. Theory and
Practice of Physical Culture 4, 11–13.
Haljand, R., Tamp, T. & Kaal, R. (1986) The
Models of Swimming Strokes and Methods
of Perfection and Control, 2nd edn. Tallinn
Pedagogic Institute, Tallinn.
Hollander, A., De Groot, G., van Ingen
Schenau, G.J. & Toussaint, H.M. (1986)
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Holmer, I. (1974) Physiology of swimming
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Huijing, P.A., Toussaint, H.M., Mackay, R.,
Vervoorn, K., Clarys, J.P. & de Groot, G.
(1988) Active drag related to body
dimensions. In: Swimming Science V,
(eds B.E. Ungerechts, K. Reischle &
K. Wilke) pp. 109 –113. Human Kinetics
Publishers, Champaign, Illinois.
Issurin, V.B. (1977) Evaluation of hydrodynamic resistance and propelling
forces in swimming. Theory and Practice
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Karpovich, P.V. (1933) Water resistance in
swimming. Research Quarterly 4, 21–28.
Kent, M.R. & Atha, J. (1975) Intracycle
kinematics and body configuration
changes in breaststroke. In: Swimming
II (eds J.P. Clarys & J. Lewillie), pp.
125 –129. University Park Press,
Baltimore.
Kolmogorov, S. & Duplisheva, A. (1992)
Active drag, useful mechanical power
output and hydrodynamic force
coefficient in different swimming
strokes at maximal velocity. Journal of
Biomechanics 25, 311–318.
Kolmogorov, S., Rumyantseva, O.,
Gordon, B. & Cappaert, J. (1997) Hydrodynamic characteristics of competitive
swimmers of different genders and
performance levels. Journal of Applied
Biomechanics 13, 88 –97.
Maglischo, E.W. (1993) Swimming Even
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View, California.
Makarenko, L.P. (1996) Fundamentals
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Swimming (eds N. Zh. Bulgakova &
L.P. Makarenko), pp. 40 – 85. Physical
Culture Education & Science, Moscow.
Miller, D.I. (1975) Biomechanics of swimming (eds J.H. Wilmore & J.F. Keogh)
pp. 219 –248. Exercise and Sport Sciences
Reviews. Academic Press, New York.
Miyashita, M. & Tsunoda, R. (1978) Water
resistance in relation to body size. In:
Swimming Medicine IV (eds B. Eriksson
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Onoprienko, B.I. (1967a) The influence of
anthropometrical data on the swimmer’s
hydrodynamics. Theory and Practice of
Physical Culture 4, 18–23.
Onoprienko, B.I. (1967b) Use of modelling
for water resistance to swimmer’s body
movement research. Theory and Practice
of Physical Culture 9, 8–9.
Onoprienko, B.I. (1968) Relationship of
hydrodynamic drag and swimmer’s
body position. Theory and Practice of
Physical Culture 9, 12–15.
Rumyantsev, V.A. (1981) Biomechanics of
Swimming. Central State Institute of
Physical Culture, Moscow.
Rumyantsev, V.A. (1982) Biomechanics of
Sport Swimming. Central State Institute
of Physcial Culture, Moscow.
Safarian, I.G. (1968) Hydrodynamic
characteristics of the crawl. Theory and
Practice of Physical Education, USSR 11,
18–21.
Schramm, E. (1959) Die Abhangigkeit der
Leistungen im Kraulschwimmen vom
Kraft-Widerstand verhaltnis. Wissenschaft Zeitschrift der Deutsche Hochschule
Von Korperkultur 161–180. Leipzig.
Sharp, R. & Costill, D. (1989) Influence of
body hair removal on physiological
responses during breaststroke swim-
ming. Medicine and Science in Sports and
Exercise 21, 576 –580.
Toussaint, H.M. & Beek, P.J. (1992)
Biomechanics of competitive front
crawl swimming. Sports Medicine 13,
8 –24.
Toussaint, H.M., De Groot, G., Savelberg,
H.H.C.M. et al. (1988) Active drag
related to velocity in male and female
swimmers. Journal of Biomechanics 21,
435 – 438.
Toussaint, H.M., de Looze, M., van
Rossem, B., Leijdekkers, M. & Dignum,
H. (1990) The effect of growth on drag
in young swimmers. Journal of Sport
Biomechanics 6, 18 –28.
Chapter 10
Propulsive Forces in Swimming
A.R. VORONTSOV AND V.A. RUMYANTSEV
The nature of propulsive forces in
swimming
The aquatic locomotion of a human is a result of the
interaction of body segments with the water. On
land a human uses the ground surface as a solid and
immobile support. Effort is applied against the
ground and the ground’s reaction transmitted to
the body makes the body move. During swimming a swimmer creates the ‘immobile support’
in the mobile fluid medium, using its density and
viscosity, and overcomes opposing resistive forces.
The nature of swimming is that it occurs in water,
which resists the swimmer’s motion through it. The
hydrodynamic resistance (HDR) manifests itself as:
(i) the force that slows down and stops the swimmer’s motion through the water (see Chapter 9); and
(ii) as a hydrodynamic reaction force to the movements
of the swimmer’s limbs through the water. This
hydrodynamic reaction force (RF) is the source of
propulsion for the swimmer’s locomotion.
The swimming velocity depends upon the magnitude and direction of the RF (or total pulling force)
created by movements of the swimmer’s working
segments, and the magnitude of the active hydrodynamic resistance. The RF created by the swimmer
constantly changes its value and direction during
the cycle of swimming motions due to the alteration of working phases and recovery phases.
Correspondingly, there are changes in the effective
pulling force—a component of the resulting RF equal
to the projection of the RF vector to the direction of
motion. The value of active HDR also changes continuously within the swimming cycle.
The interaction within the swimming cycle of
these two horizontal forces (effective pulling force
and active hydrodynamic resistance), as a rule not
equal at any one moment, may be described by
the equation of set non-stationary activity of a
swimmer’s body in fluid flow (Toussaint et al. 1998;
Cappaert 1998; Kolmogorov & Lyapin 1998):
FP(effective)(t) – FDA(frontal)(t) = (m0 + ∆m)dv(CM)/dt
(10.1)
where FP(effective)(t) = momentary value of total effective propulsive force developed by the swimmer’s
propelling segments (result of working movements
of arms, legs and body); FDA(frontal)(t) = momentary
value of frontal component of hydrodynamic resistance affecting the swimmer’s body; m0 = body
mass; ∆m = added water mass of an inertial origin;
and dv(CM)/dt = momentary acceleration of body
centre mass.
It follows from Eqn. 10.1 that when FPropulsive =
FDrag the swimmer moves with uniform velocity,
when FP > FD the swimmer accelerates, and when
FP < FD the swimmer decelerates.
To generate high propulsive force during swimming is not an easy task. Not all components of the
resultant RF contribute to an effective RF (pulling
force) due to deviation of the vector of the reaction force from the swimming direction at certain
moments of pulling actions (Schleihauf 1979;
Rumyantsev 1982; Cappaert & Rushall 1994). At
the same time a substantial part of the mechanical
energy of the pulling actions is lost in transfer of
kinetic energy to the water mass which the swimmer
uses as a support. As a result, only a portion of the
205
206
locomotion
mechanical work performed by a swimmer is used
effectively to overcome HDR. As we shall demonstrate later in this chapter, it is not enough simply to
press against the water as hard as possible. Instead,
the aim should be to adroitly change the direction of
movement throughout the course of the pull so that
the vector of the resulting RF remains as close to the
swimming direction as possible.
Biodynamic details of pulling
movements
The propulsive forces in swimming originate from
muscular contractions (muscle draught). When the
biokinematic chains ‘shoulder-forearm-hand’ and ‘hiplow leg-foot’ begin to move they encounter hydrodynamic resistance. When the muscle draught
balances the external hydrodynamic RF force and
the latter balances the HDR, the body general centre
of mass (GCM) begins to accelerate in the direction
of locomotion. Thus the hydrodynamic reaction
force transforms into a propulsive (pulling) force.
Since the pulling movements are rotational movements of extremities in the joints the system of
forces may be expressed by the following equation
(the displacement of the axis of rotation conditionally accepted as zero—see Fig. 10.1):
0
rinert.
ϕ
r
rm
Q
Finert.
Fm
F
rQcosϕ
mg
rinert.cosϕ
Fig. 10.1 Forces and their levers (relative to the axis of
rotation, 0); illustration to Eqn. 10.1.
Fmrm = Iω̄ + Fr – mgrinertia cos φ + QrQ cos φ
(10.2)
where Fm = resultant force of muscle draught (N); rm
= lever of the resultant muscle force (m); I = moment
of the inertia of the arm (kg · m2); F = resultant
hydrodynamic reaction force (N); r = lever of the RF
(m); mg = gravity (N); rinertia = radius of the arm inertia force (m); Q = hydrostatic force (N); rQ = lever
of the hydrostatic force (m); φ = relative angular
position of the arm (degrees); and ω̄ = angular acceleration of the arm (± degrees per second per second;
may be positive as well as negative).
If we assume that during underwater pull the
gravitational and hydrodynamic forces are equal,
opposite and colinear the equation is simplified:
Fmrm = Iω̄ + Fr
(10.3)
It follows from this equation that the reduction of
length of the levers of external forces (inertia and
hydrodynamic reaction) by bending the arm at the
elbow joint leads to increase of the dynamic and
time-spatial characteristics of the arm pull and
requires smaller muscle torque. Miller (1975) represented Eqn. 10.2 in the following form:
Fmrm ≈ mr 2inertia ω̄ + CDr3 ω2
(10.4)
where Fmrm = torque of muscular force; ω̄ = angular
acceleration of the arm (or arm segment); m = arm
(arm segment) mass (kg); and CDr3ω2 = torque of the
hydrodynamic reaction created by the arm (or arm
segment).
If it is assumed that the hand velocity is roughly
proportional to the angular velocity in the shoulder
multiplied by the distance between hand and shoulder (= r), it follows that the torque of hydrodynamic
RF varies as a cube of the length of its lever while
the torque of inertia varies as the square of rinertia.
Miller (1975) supposed that corresponding changes
in pulling technique (decrease of rinertia and r and
increase of ω) would improve the efficiency of the
pulling action. Muscular draught is applied to the
shoulder close to the axis of rotation (Fig. 10.2) and
the lever of muscle force is small. The resultant RF
is applied to the distal portion of the arm and its
lever is several-fold longer in respect to the lever of
muscle draught. By arm flexion a swimmer changes
the ratio of forces applied to opposite ends of the
propulsive forces in swimming
207
Fm
l1
l2
Fig. 10.2 The formation of the muscle
draught torque and RF torque during
arm pull:
I· ω + RF · l2 = | –Fmuscle · l1|
where ω = angular acceleration.
bone lever and is able to balance greater RF torque
by smaller muscle torque when the arm is bent. In
freestyle and butterfly the elite swimmers demonstrate maximal elbow bending (the angle between
shoulder and forearm) in the middle (90 –120°) portion of the pull.
As may be seen from Eqn. 10.4, pulling patterns
with consecutive flexion–extension of the arm
have an obvious biomechanical and hydrodynamic
advantage over pulling patterns without movements in the elbow and wrist joints.
1 Movement of the elbow joint allows a selective
increase in the angular velocity and acceleration of
the hand and forearm without involving the most
massive segment of the arm, i.e. the shoulder. Pulling patterns with elbow bending require much less
muscle torque to create an equal RF and an effective
pulling force than arm pulls without elbow bending.
2 Bending the elbow and wrist joints provides efficient space orientation of the propelling segments
(Counsilman 1968; Makarenko 1975; Schleihauf
1979). It increases the working surface area of the
pulling segments (projection of these segments to
the direction of the pull) and makes it possible
to steer the propulsive forces in the direction of
swimming.
3 The strength of the arm bent at the elbow joint is
significantly higher than that of a straight arm.
Measurements of maximal isometric strength in
RF
boundary postures, imitating the distinct phases
of arm pull, shows that bent arm pull creates on
average a 20% greater force than ‘straight arm pull’
(Butovich & Chudovsky 1968; Vorontsov 1981). It
is possible that by bending the elbow, the direction
of torque in the shoulder joint changes. This could
imply that more muscles can deliver work in the
shoulder joint (Toussaint et al. 1998).
4 In the course of the arm pull the movements of the
arm joints are coordinated in a pattern which provides consecutive achievement of maximal angular
velocities in different joints. This avoids excessive
loading of the arm muscles, which work in a more
economical way. The catch phase is performed by
simultaneous extension in the shoulder and flexion
in the elbow/wrist joint. At the beginning of the
backward pull (downsweep) the hand and forearm
accelerate due to arm bending in the elbow joint,
while the shoulder moves with low angular velocity
and gradually passes from a streamlined position to
a resistive position.
During the insweep the shoulder begins to accelerate its rotation while the angle between the hand
and forearm remains relatively constant. Thus the
swimmer uses hand and forearm as a single blade.
In the main phase, as the shoulder rotation decelerates, the acceleration of the forearm at the elbow
joint begins. The forearm performs a fast extension
of the elbow joint (push), during which the hand
208
locomotion
slows down its rotation and attains its optimal space
orientation. This is the moment when the swimmer’s arm delivers the highest magnitude of RF and
effective pulling force. After this working part of the
pull is completed the exit of the arm from the water
is performed by movement at the shoulder joint.
5 The pulling pattern with alternate elbow bending
and extension provides a gradual increase of hydrodynamic reaction force and its propulsive component in the initial part of the pull, stabilization in the
middle part, and a sharp increase to the maximum
force at the end of the pull. In pulling patterns without movements in the elbow and wrist joints the
hydrodynamic force decreases significantly after
the arm passes the middle of the pull.
(a)
RFtotal = RFeffective
Concepts of propulsion in swimming
α= 90
Theory of the straight ‘oar-like’ arm pull (OLP)
(b)
This theory stems from striving to convert 100%
of the hydrodynamic reaction force into effective
propulsive force. It follows from Newton’s Third
Law of Motion that the most efficient types of pull
are those employing a straight movement of the
hand (and forearm) along the direction of swimming motion under the mid-line axis of the body,
with the arm–forearm pitch close to 90° relative to
the pulling direction (Fig. 10.3a,b). Thus during the
oar-like pull the propulsive force is created almost
entirely by pressure (form) resistance. The magnitude of propulsive force (RF) may be derived from
Eqn. 9.1: RF = 1/2 ρV2CDS, where ρ = water density,
V = speed of the water flow interacting with the
body, CD = the hydrodynamic coefficient of the
propelling segment and S = the surface area of the
propelling segment.
For several decades the role of frontal (form)
resistance was deemed paramount in describing
the origination of propulsive forces in swimming
(Cureton 1930; Kiphut 1942; Silvia 1970). The principles of Newtonian mechanics (action-reaction
principle, principle of conservation of momentum,
principle of proportionality) were employed to
prove that straightline arm pull (‘oar-like pull’—
OLP) is the most efficient, as the direction of the vector of hydrodynamic RF created by the swimmer’s
Fig. 10.3 (a) Oar-like pull (side view). (b) Contribution of
the frontal drag force (RFtotal) on the hand into effective
RF.
arm coincides with the direction of swimming
motion. It was assumed that in OLP the effort which
the swimmer applies to the water maximally transforms into forward propulsion when the direction
of the vector of resultant RF maximally coincides
with the direction of swimming (RFeffective = RFtotal).
Any deviation of the swimmer’s arms during pull
from a straightline direction was interpreted as a
technical error or as a movement to compensate for
deficiencies in the structure of the human motor
apparatus, which is not perfect for aquatic locomotion. This view still has its adherents among scientists and coaches (see, e.g., Rushall et al. 1998).
The lift and lift-and-drag theories: curvilinear
(propeller-like) arm pull (PLP)
The theory of OLP presumes that the swimmer
should maintain the maximal surface area of the
propelling segments (CD · S), and constantly increase the velocity of the pull and pressure created
by these segments during the pulling motion.
Actually the hand velocity and pulling effort (RF)
propulsive forces in swimming
209
Tcycle
F2
Ipull
F1
Trec
T1
Fminimal
Tpull
Tminimal
T2
Fig. 10.4 Typical intracycle dynamic
of pressure force on swimmer’s hand
during front crawl.
demonstrates two or three large pulses, with stabilization and even a transient decrease in the middle
part of the arm pull. Figure 10.4 shows the typical
intracyclic changes of the pressure developed by a
swimmer’s hand during the front crawl. Such intracyclic pressure dynamics bring into question the
importance of the frontal reaction force as the sole
or main propulsive force in aquatic locomotion.
The introduction of objective methods of research
and biomechanical analysis in the late 1960s and
early 1970s revealed significant deviations of the
hand trajectory in both vertical and transverse
planes from the ‘optimal’ direction of locomotion in
elite swimmers (Fig. 10.5a). These deviations need
to be explained.
Opponents of the straight pull used as an argument the principle of ‘immobile support’, which
presumes that efficient pulling actions employ complex trajectories of working movements so that at
every point of the pull the working segments of the
arms and legs interact with standing, immobile
water. As soon as a swimmer begins to apply force
against the water the latter starts to move in the
direction of the hand motion, leading to a decreased
velocity difference between hand and water and
decreased efficiency of the pulling action. Therefore,
in order to create high RF (to ‘find’ efficient supportive reaction), the pulling segments should interact at
every point of the working movement with standing, immobile water. This condition is satisfied when
pulling actions are performed not exactly linearly
backwards, but employ a complex curvilinear trajectory. If one considers swimming movements in
the orthogonal coordinate system (Fig. 10.5b), it
appears that during pulling actions the working
segments of the arms and legs accomplish movements not only straight backwards along the x-axis,
but also across the transverse (z-y) and vertical (x-y)
planes. During the working phase of swimming
motions the arm segments interact with threedimensional (3-D) water flow at some angle of attack
and change their leading edge 2–3 times (depending
on the swimming stroke). Belokovsky (1971) showed
that in synchronized swimming the effective pulling
force and high swimming velocity (e.g. 16 –17 s for
a 25-m swim) may be achieved by using so-called
‘standard’ figure 8-like sculling patterns without
any significant backward displacement of the swimmer’s hands. The magnitude of the total and effective propulsive force in this case depends upon the
pitch of the hands, the working trajectory, and the
velocity of transverse hand movements.
Counsilman (1969, 1971), using an analysis of
underwater movies, found that world-class swimmers perform arm pulls as sculling movements with
very complex curvilinear trajectories in 3-D space.
In these pulling patterns the hand and forearm
perform significant vertical and transverse movements and continuously change the direction of
the pull and their pitch (the angle of attack and leading edge) relative to the water flow. Counsilman
concluded that it is virtually impossible to find
210
locomotion
z
x
y
y
Front view
Side view
Hand velocity (m · s–1)
3
x
Bottom view
2
z
1
0
5
10
(a)
15
t (1/22.5s)
x
z
z
y
x
y
c
a
a
b
f
b
b
e
d
d
e
f
c
d
c
a
(b)
Side view
f
e
Bottom view
Front view
Fig. 10.5 (a) Example of a swimmer’s fingertip trajectory pattern (front crawl) and absolute hand speed date.
(b) Trajectory of the hand relative to the system of orthogonal coordinates in front crawl arm pull. (Adapted from
Schleihauf 1979.)
propulsive forces in swimming
V
L
RF
L
–
2
Area of low
pressure
RF
3
–
D
D
+
211
–
+
–
+
1
Area of high pressure
Fig. 10.6 Bernoulli’s principle: origin of hydrodynamic lift on (left) a hydrofoil and (right) the hand (according to Reischle
1979). (1), area of stagnant water—high pressure; (2), area of low pressure above the hand; (3), area of turbulence (low
pressure) in the wake of the hand.
instances when the hand and forearm are disposed
to the water with an angle of attack exactly 90° to the
pulling direction. He made an assumption that the
major contributor to human locomotion in water is
the hydrodynamic lift force (normal component of
resulting hydrodynamic reaction), which originates
when the hand and forearm move at an angle of
attack to the water flow (to pulling direction). In this
case both segments interact with water flow as a
hydrofoil.
Counsilman cited Bernoulli’s principle to explain
the nature of propulsive forces in swimming
(Fig. 10.6). According to this principle the hydrodynamic lift originates as the result of the difference between water flow velocities on the upper and
lower surfaces of the hand (and forearm). Counsilman estimated that the hydrodynamic profile of
the human hand creates a significant lift force. The
properties of the hand and forearm as hydrofoils
were also studied by Schleihauf (1974), Bartels and
Adrian (1974), Reischle (1979), Onoprienko (1981)
and Rumyantsev (1982), all of whom shared the
opinion that hydrodynamic lift makes a significant contribution to swimming propulsion. Issurin
and Kostyuk (1978) found that during swimming
at maximal velocity backward displacement of the
hand (the projection of its trajectory on the x-axis)
comprises only 25% of the length of its absolute
trajectory. The average velocity of backward displacement of the hand was found to be less than the
average forward velocity of body motion. At the
same time the absolute hand velocity relative to
the water flow achieved 3 – 4 m · s–1. By using transverse and vertical sculling movements, swimmers
achieve a high magnitude of lift to create high
resulting RF without significant displacement of
water mass backwards, and prolong the duration of
action of the propulsive force. These theoretical
speculations and experimental data formed the
basis of the theory of curvilinear, propeller-like pulling patterns (PLP).
Three-dimensional analysis of the absolute movements of limb segments and the core body in relation
to orthogonal coordinates has allowed an understanding of the hydrodynamic nature and complexity of propelling forces (Schleihauf 1974, 1979; Wood
1979; Cappaert 1993, 1998). This analysis showed
that in sport swimming no examples could be found
of pulling patterns in which exclusively the frontal
(pressure) or normal (lift) component of hydrodynamic reaction was used to create propelling force.
Propulsive forces are created by contributions
of both normal and frontal components of hydrodynamic reaction. The relative contributions of
drag and lift forces to a swimmer’s propulsion vary
significantly between distinct phases and moments,
between individuals, and between swimming
strokes. By changing the pitch of the hand it is
possible to steer the resultant propulsive force in
the direction of swimming.
Both drag and lift forces can be derived using the
following equations of hydrodynamics:
212
locomotion
FD = 1/2 ρV2CDS
(see Eqn. 9.1)
L = 1/2 ρV2CLS
(10.5)
where L = lift force, CL = coefficient of lift of the propelling segment, S = surface area of the propelling
segment, and V = absolute velocity of the propelling
segment relative to water flow. It follows from Eqn.
10.5 that to create high total and effective pulling
force the following conditions must be satisfied.
1 There should be a high velocity of interaction
of the propelling segments with water flow (both
frontal and lift forces are proportional to the square
of the propelling segment’s velocity).
2 There should be optimal hydrodynamic orientation (pitch) of the segments relative to the water
flow (selective maximization of CD and CL due to the
continuously changing direction of the pull).
3 There should be optimal balance between the
‘size’ of the segment’s projection on the pulling
trajectory and the ‘wing’ surface area creating lift.
4 The pulling trajectory should have optimal amplitude and direction.
Counsilman (1977), influenced by the studies of
Schleihauf, also came to the conclusion that both
drag and lift forces are equally important in creating
the effective propulsive force. Thus originated the
lift and drag theory of swimming propulsion. The
results of Schleihauf’s studies on the relationship of
hydrodynamic drag and lift forces developed by the
biokinematic pair ‘arm–forearm’ facilitated a better
understanding of human aquatic locomotion and
were used as the basis for subdividing arm pulls
into four phases: downsweep, insweep, backsweep
and upsweep.
The vortex theory and the complex mechanism
theory of swimming propulsion
The vortex theory is widely used for the description and analysis of swimming in fish, and was
introduced into sport swimming by Colwin (1984,
1992), who supported his theoretical speculations
on vortex theory by some video data obtained in
sport swimming. He proposed that part of the
kinetic energy lost by swimmers to the water mass
could be reabsorbed into pulling action from water
vortices.
More recently Toussaint et al. (1998) expressed the
opinion that neither drag nor lift theories give a
complete explanation of the mechanism of pulling,
and supported this by successful experiments on
visualization of water flow around the swimmer’s
arm. They assumed that since the pulling segments
of arms and legs move in a quasi-steady water flow,
the vortex theory may explain better the mechanism
of action of the propulsive force. This is especially
true for transitional periods of the pull, when the
hand and forearm change sharply the direction
(leading edge) and velocity of the pull. The mechanism of how the starting vortex and bound vortex
(circulation) facilitate the pressure differential and
thus increase propulsive force is shown in Fig. 10.7
(the so-called condition of Zhoukovsky).
The latest studies in aerodynamics have disproved the Bernoulli principle as an explanation of
lift. This principle assumes equal transit time for
particles over and under the aerofoil. In fact, the
upper-surface transit time is always less than that
below (Denker 1998). The generally accepted theory
taught that the wing begins to produce lift as result
of a ‘starting vortex’, which is formed behind the
trailing edge as the wing moves forward. This vortex causes circulation to appear around the wing.
With this circulation superimposed on passing flow,
the upper-surface air velocity becomes greater than
that below. The flaw in this explanation is that there
are no known physical principles to explain how the
starting vortex can cause circulation. All that is
known is that a starting vortex really does occur, the
above-wing flow does have a greater velocity, and
the magnitude of the lift force is much greater than
would follow from Bernoulli’s principle—even a
flat aerofoil can create effective lift under certain
conditions.
Experiments in water tanks confirm that both lift
and drag forces occur when hand and forearm casts
are exposed to water flow or are moved relative to
standing water (Schleihauf 1974, 1979; Grinev 1977),
and both these forces contribute to propulsion in
aquatic locomotion. In practice, it is of little concern exactly what is the reason of the lift, and which
theory is most accurate.
Recently, the most widely accepted theory of
swimming propulsion is the lift-and-drag theory of
propulsive forces in swimming
Accelerated motion
213
Motion at uniform velocity
Flow V
Circulation
(bound vortex)
Leading-edge vortex
Lift
Bound
vortex
Starting
vortex
– Lift
–
u
+
u
P1
P2
+ P2
P1
+
u
–
+
Trailing-edge
vortex
–
u
(a)
(b)
Fig. 10.7 The Vortex Theory: circulation (bound vortex) around the hand and the system of vortices behind the rear
surface of the hand create lift (condition of Zhoukovsky). Flow velocity above the ‘wing’: V1 = V – u. Flow velocity below
the ‘wing’: V2 = V + u. Pressure differential: P = P2 – P1 = 1/2 (V12 – V22) = 2Vu (where u = flow velocity in bound vortex).
propeller-like pull (PLP). Hence, until a better
theory of aquatic propulsion is developed, we
would like to focus on the lift-and-drag concept in
order to discuss the following topics:
• under what conditions does the hydrodynamic
reaction force originate on working segments?
• what is the potential of arm and leg segments to
create propelling forces? and
• what are the factors determining the efficiency of
pulling actions? etc.
Hydrodynamic potential of arm
segments
As mentioned above, propulsive forces created by
the swimmer are the result of the interaction of
arm and leg segments with the water flow during
pulling movements. These propulsive forces by
their nature are forces of hydrodynamic resistance.
The ratio of forces created by distinct segments of
limbs is determined as:
Fi+1/Fi = Si+1 Ci+1 Vi+12/Si Ci Vi2
(10.6)
where Fi and Fi+1 = hydrodynamic forces (N) of
segments i and i + 1; Si and Si+1 = frontal surface
area (m2) of segments i and i + 1; Ci and Ci+1 = non-
dimensional drag coefficients of given segments;
and Vi and Vi+1 = velocities of segments’ interaction
with water flow. The shoulder has the least S × C
product and least propulsive potential. The forearm and hand have approximately equal S × C
products since the smaller support area of the
hand is compensated by a greater drag coefficient
CDhand (Butovich & Chudovsky 1968; Bagrash et al.
1973).
A decisive factor in determining the relationship
of hydrodynamic forces created by the arm segments is the velocity of their interaction with water
flow. The difference in angular and linear velocity of
arm segments relative to the axis of the shoulder
joint determines the difference in absolute velocity
of the segments’ interaction with the water flow.
Thus it determines the magnitude of total RF created by each arm segment.
The angular and linear velocity increases from
shoulder to hand proportionally with the increase
in the radius of rotation. Butovich and Chudovsky
(1968) and Makarenko (1975) showed that the
average intra-cyclic linear velocity of the shoulder
and RF created by the shoulder are negligible.
Moreover, at some points in the pulling action the
shoulder creates a drag to the forward motion. Due
214
locomotion
Number of lead
P (g·cm–2 ) I
II
III
1
2
3
4
5
6
44.5
54.3
26.7
25.0
14.7
5.8
6.1
5.9
5.4
6.0
5.7
4.4
4.1
3.3
2
1.9
1.6
14.4
to active movements in the elbow and wrist joints
the forearm and hand have a significant advantage
over the shoulder in terms of angular and linear
velocity. Thus only the forearm and hand of a swimmer create significant hydrodynamic reaction forces
(i.e. propulsive force).
Miller (1975), using a mathematical model of the
front crawl arm pull with bending of the elbow,
found that the ratio of hydrodynamic forces of hand
and forearm is about 2.5 : 1. Since she used a model
which did not include hand movement at the wrist
joint, the hand and forearm were assumed to have
the same angle of attack relative to the water flow. In
reality a swimmer uses minor hand movements at
the wrist joint to give the hand the most efficient
position (Schleihauf 1979). Thus it may be assumed
that the ratio of hydrodynamic forces created by
hand and forearm should be greater than the above
value.
Bagrash et al. (1973), using tensiometry, measured
hydrodynamic pressure on distinct arm segments
during front crawl swimming (46 male well-trained
swimmers). The experiment included:
1 tethered swimming using straight arm pull;
2 tethered swimming using pull pattern with elbow
bending; and
3 ‘natural’ swimming.
Figure 10.8 depicts the location of pressure leads
and corresponding magnitudes of maximal hydrodynamic pressure during tethered and free swimming (averaged for 20 strokes).
Multiplying the maximal pressure developed by
a segment (for hand, readings of lead 1; for forearm,
mean value of leads 2 and 3; for shoulder, mean
Fig. 10.8 Location of the tensioleads
on a swimmer’s arm and maximal
values of the pressure. (Adapted
from Rumyantsev 1984.)
value of leads 4 – 6) by the surface area of a segment
and corresponding relative drag coefficients it is
possible to obtain the maximal relative hydrodynamic forces of arm segments. The magnitudes
of drag coefficients at an angle of attack of 90° were,
respectively: for hand 1.0, forearm 0.7, shoulder
0.6 (data obtained during exposure of plaster cast
of arm segments to water flow in the water tank;
Butovich & Chudovsky 1968).
Table 10.1 gives the values of hydrodynamic
forces after correction (Rumyantsev 1982). These
measurements show that in conditions of ‘natural’
swimming (III) the hand creates about 70 –75% of
the total hydrodynamic force of the arm. A further
20% or so is created by the distal half of the forearm.
(N.B. These results were obtained for ‘flat’ flow
using arm casts exposed to water flow at a 90° angle
of attack and the sole reaction force acting on the
arm segments is frontal (form) resistance.) The conclusion may thus be made that the major propelling
Table 10.1 Maximal intracyclic hydrodynamic force of
arm segments during front crawl swimming. (From
Bagrash et al. 1973; adapted by Rumyantsev 1982.)
Arm segment
Hand
Forearm
Shoulder
S (cm2)
Relative
Cx
F—I
(N)
F—II
(N)
F—III
(N)
151
221
217
1.0
0.7
0.6
65.8
24.1
5.0
79.6
23.6
5.1
61.3
15.6
4.4
Cx = drag coefficient. F—I = force during tethered
swimming using straight-arm pull. F—II = force during
tethered swimming using elbow bending. F—III = force
during ‘natural’ swimming. S = surface area.
propulsive forces in swimming
forces during swimming are generated by the hand
and distal half of the forearm. It means that in
analysing hydrodynamic forces we can neglect any
force produced by the shoulder (Schleihauf 1979;
Wood 1979). Schleihauf (1979) determined the effective propulsive force delivered by arm segments at a
swimming speed of 1.66 m · s–1. The average propulsive force delivered by the hand was 48 N, and
the average effective forearm propulsive force
was 24 N.
Drag and lift during different phases of
pulling actions
Effect of form and orientation of arm segments on
hydrodynamic forces
Studies performed in water tanks using casts of the
hand with differently shaped palms and finger
Fig. 10.9 The most efficient
hydrodynamic forms of the hand.
(From Makarenko 1996.)
215
positions (Counsilman 1968; Makarenko 1975;
Onoprienko 1981) show that the most effective
combinations for creating a high hydrodynamic
reaction are (Fig. 10.9):
1 flat palm with fingers and thumb held together;
2 flat palm with thumb apart; and
3 flat palm with fingers and thumb held slightly
apart.
Forms 1 and 2 are more effective for those phases
where the hand moves at sharp angles of attack to
the pulling direction and works as a hydrofoil.
Onoprienko (1981) stressed the important role of the
abducted thumb for fixing the hand at the wrist joint
and increasing the rigidity of the hand. Form 3 has
the advantage for phases where the hand moves
relatively straight backwards at an angle of attack
> 60° (an increase of the frontal hydrodynamic
force despite a decrease of CDx when the fingers
are slightly apart may be attributed to the greater
216
locomotion
Lift
RF
Lift
Drag
V of flow
Drag
RF
V of flow
α= 45°
α=30°
ψ = 270°
Lift
V
RF
Drag
ψ = 315°
ψ = 225°
ψ= 180°
ψ = 0°
ψ= 45°
ψ= 135°
ψ=270°
α=45°
ψ = 90°
Fig. 10.10 Sweepback angles and angles of attack of the hand.
supporting surface area). Analysis of underwater
movies and video recordings (Counsilman 1968,
1977; Haljand 1984; Haljand et al. 1986) shows that
expert swimmers generally perform pulling actions
with some spreading of the fingers. The reason for
this is still unknown. It may be that any advantage
in hydrodynamic reaction force when the fingers
are held tightly together in a strong water flow is
cancelled out by the excessive energy spent in keeping the fingers together.
The orientation (pitch) of the arm–forearm relative to the 3-D flow is an important factor in determining the ratio of drag and lift forces, the total
magnitude of the RF and the effective pulling force.
Schleihauf (1974, 1979) exposed plaster casts of the
hand to water flow in a tank to analyse the influence
of the pitch of propelling segments on the magnitude of hydrodynamic forces. He considered the
arm–forearm model in terms of the characteristics
of an aerofoil, namely the angle of attack (α) and
sweepback angle (ψ; French tangage). For a swimmer
the angle of attack is the angle formed by the inclination of the propelling surface (arm and leg
segments) to the direction of the pull, while sweepback angle defines the leading edge of the propelling segment.
Figure 10.10 depicts the angles of attack and
sweepback angles of the hand (arrows show the
direction of flow). Analysis of the forces and hydrodynamic (drag and lift) coefficients used a system
of coordinates where the x-axis related to the flow
direction.
propulsive forces in swimming
Schleihauf (1979) introduces the lift-to-drag index
to assess the predominant contribution of these
two forces in the momentary value of the resultant
RF:
L/FD = 1/2 ρCDyV2S/1/2 ρCDxV2S
= CDy/CDx
(10.7)
where CDy = momentary value of coefficient of lift of
the propelling segment, and CDx = momentary value
of the drag coefficient.
This formula may be used to determine the lift
and drag ratio in resultant RF for distinct phases of
the arm pull and for the entire pull. If the value of
the index > 1, then lift predominates; if < 1 then the
drag component is greater.
Frontal component of the hydrodynamic RF
(frontal drag, FD)
In experiments involving streamlining the hand
casts and increasing the angle of attack the coefficient of the frontal force, CDx, increases exponentially and achieves its maximum at an angle
of 90°. The form of the propelling segment and
the sweepback angle also influence the magnitude of CDX and FD at different angles of attack
(Table 10.2).
217
Normal component of hydrodynamic reaction—
hydrodynamic lift (L)
Streamlining of the hand by water flow creates a
small (|CDy| < 0.2) normal force even at α = 0°
and ψ = 90° (Reischle 1979; Schleihauf 1979). With
increased angle of attack (α) up to its critical value
(30 –35°) the coefficient of normal reaction (CDy) also
increases, but beyond these critical values of α it
again decreases to 0 at a 90° angle of attack.
Changes in the form of the propelling segments,
angle of attack and sweepback angle cause much
greater variation in the normal component of the
hydrodynamic reaction than the frontal component
(Table 10.3). The greatest variation of CDy due to
changes of magnitude of the sweepback angle was
found for angles of attack below 60°. For angles
of attack greater than 60° the absolute values and
dynamics of CDy become very similar at different
sweepback angles.
Separation of the fingers significantly decreases
the normal component (lift), while thumb abduction
increases the lift. The maximal value of CDy for the
hand occurred with the thumb abducted to 75%
of its maximal amplitude (Schleihauf 1979). It may
be concluded that when it is necessary to create
significant lift, as in sculling movements (α < 35°),
the most efficient hand position is with the fingers
held together and the thumb apart.
Table 10.2 The impact of the form of the propelling surface and sweepback angles on the magnitude of frontal reaction at
given angles of attack.
Authors
Method
Position of fingers
ψ°
α°
Cx′maximal
Schleihauf (1979)
Hand casts exposed to
flow in water channel
Thumb apart from fingers
0
90
180
270
0
75–90
90
80–90
70–80
85
1.35
1.40
1.30
1.40
1.15
90
90
90
90
1.10
1.07
90
90
1.07
Fingers 4–6 mm apart,
thumb apart
Wood (1979)
Hand casts, aerochannel,
V = 40 m · s−1
Fingers together
Fingers tightly adducted,
palm concave
Fingers apart
ψ° = sweepback angle; α° = angle of attack; Cx′ = hydrodynamic coefficient of frontal RF.
218
locomotion
Table 10.3 Impact of the form of the propelling surface and its sweepback angle on the maximal normal component of
hydrodynamic reaction at given angles of attack.
Authors
Form of propelling segment and finger positions
Schleihauf (1979)
Hand cast
Fingers together, thumb abducted 90°
Fingers together, thumb abducted 67.5°
Fingers 3.2 mm apart, thumb at 67.5°
Fingers 6.4 mm apart, thumb at 67.5°
Fingers together, thumb at 45°
Wood (1979)
Hand-forearm cast
Fingers together
Fingers together, hand concave
Fingers apart
ψ°
α°
Cy′maximal
0
90
180
270
0
0
0
0
15
55
30
35
40–45
45–50
45–55
50
0.85
0.65
0.85
1.10
0.80
0.70
0.50
0.70
0
90
180
0
90
180
0
90
180
55
50
35
55
50
35
60
55
15
0.60
1.07
0.46
0.68
1.01
0.57
0.53
0.88
0.44
ψ° = sweepback angle; α° = angle of attack; Cy′ = coefficient of the lift (normal force).
The resulting hydrodynamic reaction force (RF)
The momentary magnitude of the resulting hydrodynamic force created by the hand and forearm
is determined by the form of the ‘hand–forearm’
connection, angle of attack, sweepback angle and
absolute velocity of the arm and forearm in respect
to 3-D water flow.
In the course of the pull a swimmer varies α and ψ
of the hand and forearm in order to use effectively
both drag and lift forces to create a high resulting RF
and effective pulling force. With an angle of attack
(α) between 10 and 35° the resulting hydrodynamic
force is created predominantly by the normal (lift)
component (CDy/CDx ≥ 1.33). Within the range
35 –55° the RF of the hand is formed by equal contributions of normal and frontal (drag) components
(CDy/CDx = 0.75 –1.33). With angles of attack of the
hand >55° the RF is formed predominantly by the
drag (CDy/CDx ≤ 0.75). When the angle of attack is
greater than 75° the resulting hydrodynamic reaction force is formed almost exclusively by the drag.
It should be stressed that most effective coefficients
of hydrodynamic reaction (CD) occur when the
angle of attack of the arm–forearm ≥30°. Swimmers
strive for this degree of flow streamlining during the
main phase of the pull. According to the data of
Schleihauf (1979) and Cappaert (1998) the angle of
attack of the hand and forearm at the instant when
they develop maximal RF and effective pulling force
is within the range 60 –75°. However, during the initial (insweep) and transitional phases of the pull
swimmers use sharp angles of attack (Schleihauf
1979).
Much smaller hydrodynamic reaction is produced when the angle of attack of the propelling
segments is ≤10 –15°. Values in this range are used
by swimmers during the parts of the recovery that
are performed under water (arm entry and exit in
front and back crawl and butterfly, forward sweep
in breaststroke).
It is worth mentioning the strong relationship
between the RF and sweepback angle of the hand.
Thus a hand orientation with α = 15° and ψ = 0°
propulsive forces in swimming
gives 31% greater RF than with α = 15° and ψ = 45°.
Increasing the angle of attack by 10° (α = 25°) at
ψ = 0° creates 8% less RF than at α = 25° and ψ = 45°
(Schleihauf 1979; Rumyantsev 1982).
Comparison of the oar-like pull (OLP)
and curvilinear pull (CLP)
It is now firmly established that efficient arm pull
patterns begin with active ‘overtaking’ rotational
movements of the hand and forearm at the elbow
and wrist joints with respect to the shoulder (Counsilman 1968, 1977; Makarenko 1975; Haljand et al.
1986). This technique is characterized by a gradual
increase of the hydrodynamic RF and its effective
component (Counsilman 1977; Schleihauf et al. 1979;
Haljand et al. 1986; Maglischo 1993). It helps to avoid
significant angular accelerations of the arm segments and sudden changes in intracycle velocity of
the swimmer. Unskilled swimmers have been found
to have a rapid increase of hydrodynamic reaction
at the beginning of the pull followed by chaotic
changes (Counsilman 1977; Schleihauf 1979).
During the preliminary phase the total RF and
effective pulling force increase gradually with an
increase of the angle of attack and velocity of the
hand and forearm. At the moment of entry into the
water the hand with fingers together creates a minor
resistive force. At the same time extension of the
arm over the head improves the streamlining of the
head and shoulders and reduces total HDR. This
effect is facilitated by the positive vertical component of the RF created by the hand.
During the transitional phase there is a gradual
decrease of the angle of attack of the hand and forearm, and the magnitude of RF and effective pulling
force also decreases.
In the middle part of the arm pull the propulsive
force is created by roughly equal contributions of
the normal and frontal components of RF. An optimal relationship of these two components is determined by a number of factors. The most important
are as follows.
1 Rules for particular swimming disciplines limit
the direction and amplitude of movements, and
their timing.
219
2 The relationship of the velocity of a swimmer’s
GCM motion to the relative velocity of the propelling segments (VGCM/Vhand). The closer to 1 is
this ratio, the greater the advantage in velocity of
interaction with water flow, the better support reaction attains the swimmer.
3 Speed-strength abilities and strength endurance
of the swimmer. These determine the changes in
kinematic and dynamic characteristics of the pulling
actions during an entire race (angle of arm flexion in
elbow joint, stroke rate, stroke distance, etc.).
4 The range of movement and flexibility of the
joints, which limit the possible variations in the position of the pulling segments relative to the water
flow and direction of locomotion.
5 Development of the kinesthetic sense (‘feeling for
water’), allowing manipulation of the parameters
of pulling actions. Schleihauf (1979) assumed that
CLP requires more perfect ‘feeling for the water’
than OLP.
Schleihauf (1979) showed that in elite swimmers
the propulsive part of the arm pull in every stroke
shows the following.
1 Patterns with exaggerated curvilinear trajectory
of arm–forearm movement:
(a) pulls with predominantly transverse movements of the hand and forearm; and
(b) pulls with significant change of the depth of
the pull.
In these pulling patterns the propulsive force is created predominantly by the normal (lift) component
of hydrodynamic reaction and efficient propulsive
force may be created in all phases of the pull.
2 Patterns with a relatively straight trajectory. Here
the propelling force is created predominantly by the
frontal pressure force, mainly in the middle part of
the pull while the hand moves backwards.
The CLP has some advantages over the OLP.
Thus in order to achieve an equal absolute velocity
of interaction with water flow the CLP utilizes a
lower relative backward velocity of the arm segments and requires much less effort to overcome
their inertia than OLP (Table 10.4 gives massinertial characteristics of the propelling segments).
This advantage of the CLP depends upon swimming velocity. During swimming at low velocities a
220
locomotion
Table 10.4 Relative mass (% of total body mass) of arm
and leg segments in adult males. (From Zatsiorsky et al.
1981.)
Segment
Mass of segment/body mass × 100%
Hand
Forearm
Upper arm
Foot
Lower leg
Upper leg
0.61
1.62
2.71
1.37
4.33
14.17
swimmer using OLP is able to achieve (by increasing relative arm velocity) the same velocity of
arm–forearm interaction with water flow as in CLP.
So the advantage of CLP will be only in the smaller
effort needed to overcome the inertia of the pulling
segments. At maximal swimming velocity, when
the relative backward velocity of the pulling segments is limited by the speed-strength abilities of an
athlete, the OLP does not allow such a high velocity
of arm–forearm interaction with the flow as in CLP.
As the external load increases with increased swimming velocity the angle of arm bending at the elbow
joint also increases (Butovich & Chudovsky 1968;
Counsilman 1977). This movement is aimed at utilizing the angles of maximal force (AMF) and is
accompanied by a deviation of the arm–forearm
trajectory from the direction of motion.
Apart from the advantage in velocity of interaction of the propelling segments with the water flow,
the CLP allows the pulling segments to find ‘still
water’ and thus increase the stroke distance while
maintaining the optimal stroke rate. Moreover, the
longer duration of arm interaction with the flow
(longer pulling trajectory) of CLP may create a
greater impulse of RF than OLP.
The main advantage of OLP is the utilization of
most effective coefficients of hydrodynamic reaction due to high angles of attack (α = 55–75°), while
CLP achieves lower values of CDx as it utilizes much
smaller angles of attack. Thus a smaller velocity of
arm interaction with water flow in OLP may be
compensated by a greater CDx. Due to effective
arm–forearm orientation and direction of pull the
OLP allows greater transformation of the hydrodynamic reaction force into an effective propulsive
force during swimming.
Thus it may be concluded that both pulling patterns have high propulsive potential. However, the
use of OLP and CLP in individuals will depend
on a number of hydrodynamic and biomechanical
(anatomical) factors.
Normal and frontal components of
propulsion in different swimming
strokes
The amount by which the hydrodynamic reaction
force may deviate from the direction of propulsion
depends on the swimming stroke. In synchrosymmetrical swimming strokes (e.g. breaststroke
and butterfly) transverse components of the hydrodynamic force are mutually discharged and vertical
components are used efficiently for body support.
In swimming strokes with alternate arm and leg
movements (front and back crawl) it is necessary to
avoid significant deviation of the hydrodynamic
reaction force from the swimming direction, since
this may cause undesirable sideways and vertical
deviation of the body and thus increase the hydrodynamic resistance. It follows that during butterfly
and (especially) breaststroke swimming, the pulling
action may be closer to a CLP and even a propellerlike pulling pattern than occurs during front and
back crawl. Assessment of the relative contribution
of the lift and drag in the resultant RF and effective
pulling force may be made on the basis of the data
given in Table 10.5. For different swimming strokes
the combination of drag and lift force and the distribution of total and effective hydrodynamic force
within the swimming cycle will vary significantly.
The lift-and-drag index, diagonality index and force
distribution index show that lift predominates over
drag force in breaststroke. In freestyle and butterfly
lift and drag forces appear to be about equally
important during the major portion of the propulsive phases of the pull. In backstroke, swimmers use
drag force more than lift force (i.e. sculling movements are less important for backstroke than for
breaststroke, butterfly or freestyle).
propulsive forces in swimming
221
Table 10.5 Characteristics of pulling motion curve-linearity in four competitive swimming strokes.
Stroke
Freestyle
Butterfly
Backstroke
Breaststroke
Diagonality
index*
Lift-and-drag
index†
Force distribution
index‡
59 ± 13
44 ± 21
47 ± 17
81 ± 9
1.04 ± 0.28
0.95 ± 0.39
0.77 ± 0.21
1.25 ± 0.21
0.82 ± 0.07
0.81 ± 0.06
0.58 ± 0.13
0.65 ± 0.13
* The diagonality index is the average angle of the negative hand line of motion and
the forward direction at the points of first, second and third maximal RF production.
† The lift-and-drag index is the average ratio of lift and drag forces (CL/CD) at the
three largest occurrences of RF.
‡ The force distribution index is the average location of the three largest occurrences
of RF expressed as a percentage of the total duration of the underwater phase of the
arm pull.
Figure 10.11a–d shows a hand propulsive force
diagram (combination of lift and drag force into
resultant RF), intracyclic dynamics and impulse of
total and effective propulsive forces in four swimming strokes (Schleihauf 1979). These graphs characterize the rhythmical structure of the pull and
values of forces applied by swimmers in distinct
phases of the pull. The largest effective propulsive
forces in freestyle and butterfly occur near the end
of the arm pull (after the hand passes two-thirds
of the pull). In breaststroke the largest effective
propulsive force occurs at the midpoint of the
inward sculling motion of the hands.
The cycle of arm movements and
phases of arm pull
The swimming cycle or cycle of swimming movements
as a multiple repeated system of movements consists of a preliminary part (recovery) and a working
part (pull). The recovery is aimed at restoring the
working posture of the arms or legs, while the pull
creates the propulsive force.
A single cycle is characterized by a beginning and
end, and intervening phases which differ in their
kinematic and dynamic characteristics and have
distinct motor objectives. The optimal duration of
each phase within the swimming cycle is necessary
for the effective coordination of swimming move-
ments and maintenance of high and relatively uniform intracyclic velocity.
Table 10.6 shows the phases of the arm cycle in
all swimming strokes. The main feature of such a
subdivision of the cycle into phases is the prevailing direction of the vector of hand velocity within
the system of immobile orthogonal coordinates
(Schleihauf 1979).
The objective of the initial phase is to prevent any
decrease of intracyclic velocity, start acceleration of
the body, and move the pulling segments to their
most effective position in readiness for the main
part. In this phase the hand and forearm work as
hydrofoils. The acceleration of the body GCM during the initial pulling phase is created in breaststroke and butterfly by leg kick (the transfer of the
pulling effort from legs to arms). In front and back
crawl this initial acceleration is accomplished by the
main phase of pull of the opposite arm (transfer of
the pulling effort from one hand to another) and
also by utilization of kinetic energy (inertia) of the
entire system.
The objective of the main phase is to achieve maximal intracyclic velocity. During the main phase the
hand and forearm maintain an optimal orientation
relative to the water flow and direction of motion.
From an anatomical point of view the main phase
can be subdivided into two parts: pull and push.
The boundary point between these parts is the
Bottom view
Bottom view
D = 74.0
D=68.5
R=87.8
R = 96.9
L= 62.6
L=55.0
V=3.0
AP=38
V = 3.3
Side view
AP = 34
Side view
L=129.1
L = 94.4
R = 136.8
R=190
V=3.8
V = 3.3
AP=41
AP = 40
D = 98.9
D=139.4
Hand force vs. time
B
Hand force vs. time
B
175
125
R
150
RE
R
RE
–RE
100
–RE
A
A
100
75
Hand force (N)
Hand force (N)
125
75
50
50
25
25
0
0
Time (1/66s)
(a)
Time (1/66 s)
(b)
Fig. 10.11 Impulse of resultant and effective reaction force in four competitive swimming strokes: (a) freestyle; (b)
butterfly; (c) backstroke; and (d) breaststroke. AP, angle of pitch (degrees); V, absolute hand velocity relative to water
flow (m · s–1); D, frontal drag component; L, lift component; RF, resultant reaction force. (a) bottom view, middle of stroke;
side view, finishing sweep motion; hand force vs. time, R, resultant force; RE, resultant effective force. (b) bottom view, inward
Side view
Side view
R = 62.9
L=25.4
D = 38.5
R=38.7
L = 56.0
Side view
R = 75.7
D=60.2
D=29.2
V=2.6
AP=30
V = 3.2
AP = 24
L = 46.0
Bottom view
V=3.2
AP=49
Bottom view
D = 40.3
L = 40.8
R = 76.9
Side view
L = 65.5
V = 3.1
L = 47.8
AP = 52
R = 71.0
D = 58.1
V = 3.6
AP = 12
V=3.0
AP=46
R = 75.8
D=58.9
Hand force vs. time
Hand force vs. time
B
R
C
D
R
RE
60
RE
80
–RE
–RE
A
40
30
Hand force (N)
Hand force (N)
B
50
60
40
A
20
20
10
0
0
Time (1/66s)
(c)
Time (1/50 s)
(d)
scull motion; side view, finishing sweep motion. (c) side view: midstroke; side view, downward sweep; bottom view, inward
sweep; side view, upward sweep. (d) side view, downward sweep; bottom view, inward scull motion. (From Schleihauf
1979.)
224
locomotion
Table 10.6 The structure of the arm cycle in competitive swimming strokes.
Phases of cycle
Pull (working part)
Swimming stroke
Initial
Main
Transitional
Preliminary part (recovery)
Front crawl 5
Back crawl 6
Butterfly
7
Downsweep
Insweepoutsweep
Upsweep
Exit and movement
above water
Breastroke
Outsweep
Insweep
moment when the hand crosses the transverse plane
(y-z) passing through the shoulder joint. The push is
the most vigorous, decisive part of the pull, and
maximal intracycle swimming velocity occurs during the last two-thirds of the push.
In the course of the transitional phase (end of the
pull) the hand and forearm create mostly vertical
and lateral reaction forces to lever out the negative
forces (gravity, inertia). Another motor objective of
the transitional phase in front crawl, backstroke and
butterfly is to achieve arm exit with minimal resistance to forward motion of the body.
The objective of the recovery phase is to restore
the initial position of the arm for the start of the next
cycle with minimal effort. The inertia of the arm segment (in butterfly and breaststroke inertia of the
upper body as well) may be utilized to minimize the
fluctuation of the intracyclic velocity.
Biodynamics of leg movements in
swimming
The role of leg movements in propulsion
Leg actions are able to create greater hydrodynamic
forces than arm actions (Butovich & Chudovsky
1968; Bagrash et al. 1973; Belokovsky & Kuznetsov
1976; Haljand 1984, 1986). There are several reasons
for this.
1 Legs possess significantly greater propelling surface area.
2 The relative movement of the feet during the
working phase has no backward part (except in
Entry and extension
forwards
Arm stretch
breaststroke). This allows a high velocity of interaction with the water flow to be developed at any
swimming velocity.
3 The muscle groups of the legs are significantly
stronger than those of the arms (Onoprienko 1981).
In sport swimming these features play a minor
role for creating effective propulsive forces. In finswimming the propelling surface area of the lower
extremities is increased more than twofold, giving
a three- to fourfold increase in hydrodynamic RF
and a 1.5- to 2-fold increase in swimming velocity
(Onoprienko 1981).
Due to the orientation of the foot and lower leg
relative to the water flow and direction of motion
these high hydrodynamic forces act mostly in a vertical direction and only a small fraction of them
acts straightforwards in the direction of motion.
Consequently, leg kick creates a smaller effective
propulsive force than arm pull. In front and back
crawl about 15% of the total propulsive force is
created by leg kick. In butterfly stroke the contribution of leg kick propulsion is greater, maybe
up to 20–25%. The exception is breaststroke, in
which approximately equal proportions of the
total propulsive force are created by leg and arm
movements.
Despite the limitations of legs as propelling
agents, leg movements create useful propulsive
forces in every swimming stroke at any swimming
velocity (Persyn et al. 1975; Onoprienko 1981).
Besides contributing to propulsion, leg movements
also perform several very important compensatory
functions (Butovich & Chudovsky 1968; Makarenko
propulsive forces in swimming
225
The values of the maximal intracycle pressure
forces for distinct leg segments are given in Table
10.7. Calculations were based on: (i) for foot—readings of lead 1; (ii) for lower leg—average readings of
leads 2 and 3; (iii) for upper leg—average readings of
leads 4, 5 and 6.
It was found that in ‘natural’ swimming the foot
created about 70% of the leg’s hydrodynamic reaction. Another 20% of RF is created by the lower leg.
The foot’s contribution to propulsion appears more
significant if one takes into consideration its advantage in space orientation in water flow (Counsilman
1977). The intracyclic dynamics of the hydrodynamic reaction force vary significantly from stroke
to stroke and from individual to individual. It may
be concluded that the main propelling segments of
the leg are the foot and distal half of the lower leg.
1975; Persyn et al. 1975; Haljand et al. 1986). They
serve to:
• neutralize the negative forces (gravity and inertia) and transverse components of hydrodynamic
reaction force made by pulling actions;
• smooth the intracycle fluctuations of swimming
velocity;
• maintain a high and streamlined body position;
• regulate the velocity and amplitude of body rotation around the longitudinal axis in front and back
crawl and around the transverse axis during breaststroke and butterfly;
• facilitate the propulsive phases of arm pull; and
• unify all movements in a single system, the swimming cycle.
Hydrodynamic potential of leg segments
The contribution of leg segments to propulsion is
determined by the velocity of their interaction with
the water flow, their surface area and their hydrodynamic coefficients. Bagrash et al. (1973) used
tensiometry to measure hydrodynamic pressure
experienced by distinct leg segments during front
crawl swimming under the following conditions,
denoted I–III:
I—during tethered swimming using straight leg kick
without noticeable knee flexion;
II—during tethered swimming with ‘natural’ leg kick;
III—during free swimming.
Figure 10.12 shows the location of tensioleads on
a swimmer’s leg and the corresponding maximal
values of hydrodynamic pressure (average for 20
cycles) in conditions I, II and III.
Table 10.7 Maximal intracyclic hydrodynamic forces
developed by the leg segments during front crawl
swimming. (From Bagrash et al. 1973; adapted by
Rumyantsev 1982.)
Leg
segments
S (cm2)
Relative
CD
F—I
(N)
F—II
(N)
F—III
(N)
Foot
Lower leg
Upper leg
185
301
580
1.0*
0.7
0.7
94.1
33.1
7.5
126.0
46.7
11.8
110.4
38.3
9.4
CD = coefficient of hydrodynamic resistance. F—I = force
during tethered swimming using straight leg kick without
noticeable knee flexion. F—II = force during swimming
with ‘natural’ leg kick. F—III = force during free
swimming. S = surface area.
* CD of the foot was conditionally accepted as 1.0.
Number of lead
Fig. 10.12 Location of tensioleads on
swimmer’s leg. (Data from Bagrash
et al. 1973.)
P (g·cm–2) I
II
III
1
2
3
4
5
6
51.9
69.5
60.9
27.8
39.3
33.1
4.3
6.0
4.0
3
5.1
3.7
1.8
2.3
2.0
1.1
1.5
1.4
226
locomotion
The form and orientation of the leg (foot) in water
flow and 3-D space
The question of the influence of the form and orientation of the leg on hydrodynamic forces remains
open. Onoprienko (1981) studied the influence of
the limited range of angle of attack on frontal resistance of the foot at a flow velocity of 2.0 m · s–1.
He found that during interaction of water flow with
the frontal surface of feet in the range of angles
60 –90° (ψ = 90°) there was moderate increase of
frontal drag (FX′ at α = 90°/FX′ at α = 60° = 1.08) due to
an increase in the propelling surface of the foot.
When water flow interacts with the internal surface
of the foot (ψ = 90°) at a 90° angle of attack (α = 90°)
there is much less hydrodynamic reaction than at
ψ = 0° (FX at ψ = 0°/FX at α = 90° = 1.28). The reduction
of frontal hydrodynamic reaction was a result of
reduction of CD with change of flow direction relative to the foot (CD at ψ = 0°/CD at ψ = 90° = 1.13) due to
a decrease in the supporting area. The change of ψ
from 45° to 90° (α = 90°) gives an increase of supporting area (from 200 to 223 cm2) and decrease of
hydrodynamic pressure from 0.32 to 0.28 N · cm–2.
As a result FX varied insignificantly.
Though leg movements are able to create a high
resultant hydrodynamic RF, due to space orientation of the foot and lower leg, the major component
of the hydrodynamic reaction is directed along the
vertical axis downwards (upwards in backstroke).
The transverse component is also significant while
the component of hydrodynamic reaction in the
direction of locomotion is small.
Since during natural swimming at high velocity
the foot of a skilled swimmer does not move backwards relative to the system of immobile coordinates (Makarenko 1975; Reischle 1979), propulsive
forces are delivered predominantly by the normal
component of hydrodynamic reaction. Consequently, leg actions develop a much smaller effective
propulsive force than arm actions (except in breaststroke and butterfly).
Coordination of joint movements of the leg
segments during leg kick
The most effective kicking patterns use movements
in all leg joints. The advantage of leg kick with knee
flexion–extension over straight leg kick corresponds
to the advantage of arm pull with flexion in elbow
and wrist over the straight arm pull.
A selective increase in the angular velocity of the
proximal segments (upper leg) has a fundamental
impact on leg kick due to the mass-inertial characteristics of the leg segments (see Table 10.4).
Transition from the distal to the proximal segment
of the leg involves a much greater increase in muscle
mass compared with a similar transition along the
arm. The muscles of the upper leg begin acceleration
of the leg during the working phase. Coordination
of the joint movements of the leg segments is characterized by an overtaking movement of the upper leg
relative to the lower leg and foot. During the crawl
and butterfly the hip begins an upward movement
while the lower leg and foot are still accelerating
downwards. This pattern of leg movement has been
called ‘whip-like’ movement. Thus during a leg kick
there is consecutive transformation of the torque of
internal and external forces from the hip joint to the
knee joint and ankle joint, with a gradual increase of
amplitude and angular velocity of segments from
the hip to the foot (Haljand 1986; Table 10.8).
The maximal intracyclic value of the leg kick’s
propelling force is recorded, as a rule, during the
second quarter of leg extension at the knee joints
(Haljand 1984). This is delivered by effective space
orientation and high angular velocity of the foot.
After this moment, if there is no need to create
significant vertical force, the swimmer can decrease
the relative velocity of knee extension and finish
the movement using leg inertia. This technique
facilitates the efficiency of the leg kick. With
Table 10.8 Angular amplitude (ϕ) and velocity (ω) of leg
kick in hip joint and knee joint during butterfly swimming
in skilled swimmers. (From Haljand 1974; adapted by
Vorontsov 1981.)
Joint
Type of movement
ϕ (E ± SD)
ω (E ± SD)
Hip
Extension
Flexion
24 ± 3
30 ± 7
140 ± 43
151 ± 64
Knee
Flexion
Extension
67 ± 19
62 ± 14
261 ± 39
420 ± 101
propulsive forces in swimming
increased swimming velocity kicking movements
with reduced amplitude and high tempo are more
efficient. A fast and narrow leg kick provides a high
velocity of foot interaction with the water flow and
reduces the negative effect of resistance and inertia
forces during leg recovery.
Contribution of the core body in
swimming propulsion
Since a swimmer’s body is subject to hydrodynamic
resistance it is important that it undergoes locomotor
reconfiguration—the ability to change its form and
rigidity in order to reduce hydrodynamic resistance (HDR) and transfer the effort from segment
to segment. Of course, this ability is developed
in humans much less than in sea mammals and
fishes. Nevertheless, it is commonly held that one
of the fundamental differences between the elite
and ordinary swimmer is the ability to reduce HDR
during swimming (Counsilman 1968; Toussaint &
Beek 1992; Maglischo 1993).
Colwin (1984, 1992) has introduced into swimming theory the term kinematic streamlining. Referring to the swimmer, this term perhaps has a
narrower meaning than locomotor reconfiguration.
It presumes the synchronization of body and limb
alignment with peaks of arm–forearm acceleration
during the pull in order to reduce: (i) the frontal surface area exposed to water flow and turbulence in
body wake; and (ii) wave resistance. Hence, propulsive forces will predominate over resistive ones (see
Eqn. 10.1) and swimming velocity will increase
significantly.
The body of a swimmer can contribute directly to
propulsion with undulating movements, especially
in the butterfly and breaststroke (Persyn et al. 1992;
Coleman et al. 1998). Coleman et al. (1998) came to
the conclusion that in breaststroke the forces calculated on the basis of instantaneous velocity
and acceleration of the body, differ in timing and
amount from the forces due to hand motion, calculated accordingly to the algorithms of Schleihauf
using drag and lift coefficients. They used visualization of water flow in the body wake to show that
added water mass may contribute to stabilization and
even increase the velocity of the body GSM.
227
Rolling of the body along its longitudinal axis in
the front and back crawl helps the swimmer to utilize the massive and strong muscles of the back and
breast and, thus, increase the muscle draught and
resultant RF. This rotation also assists recovery of
the opposite arm over the water and reduces transverse movements of the arms.
Characteristics of a rational swimming
technique
Countless attempts to quantify the ‘average’ values
of spatial, time-spatial and dynamic (kinetic)
characteristics of pulling and kicking patterns in
world-class swimmers have failed due to the huge
variability of these parameters (Counsilman 1968,
1977; Makarenko 1975; Schleihauf 1979; Schleihauf
et al. 1988; Maglischo 1993). This variability stems
from the significant differences demonstrated by
world-class swimmers in body type and composition, level of basic and complex physical abilities
(flexibility, maximal strength, rapidity, speedstrength, explosive strength, etc.). Nevertheless, it is
possible to establish certain principles and qualitative characteristics of a rational swimming technique. Individual techniques should satisfy these
principles in order to develop a highly effective propulsive force and achieve high swimming velocities.
Effective use of lift and drag to create a high
supportive RF
Effective pulling patterns employ complex curvilinear or diagonal motions in the course of which a
swimmer constantly changes the pitch of the arm–
forearm and the direction of motion. Thus, lift and
drag forces are combined in a high resultant RE and
effective pulling force. At every point of the curvilinear pulling trajectory the propelling segments
interact with the standing undisturbed water and
shift a larger mass of the water over a shorter distance.
The smaller the backward displacement of the propelling segments in respect to the immobile system
of orthogonal coordinates, the higher the efficiency
of the working movements. In the front crawl, topclass swimmers demonstrate a backward displacement of the hand within the range 0.4 – 0.5 m while
228
locomotion
less skilled swimmers have hand displacements of
0.6 – 0.7 m and more (Issurin & Kostyuk 1978).
‘High elbow’ position during arm pull
One of the distinct features of a rational swimming
technique is an arm pull with a high elbow position
relative to the hand. From the point of view of
hydrodynamics, an overtaking rotational movement
of the arm–forearm relative to that of the shoulder
(elbow bending) gives working segments their most
efficient form and position (increase of CD hand, Shand
and CD forearm, Sforearm) in the water flow and provides high resultant RF. The movement of the elbow
joint also facilitates muscle draught to balance the
high value of hydrodynamic reaction.
Using angles of maximal force during pulling
actions: coordination of joint movements
The biomechanical chains of the human motor
apparatus are able to exert maximal joint torque
in isolated movements when the limb’s segments
occupy a particular position relative to each other
and the core body. In this position the direction of
muscle draught and the starting length of the muscles are optimal for delivering the maximal effort.
The angles at which segments are disposed relative
to each other when the maximal force (muscle
torque) is generated are called the angles of maximal
force (AMF). During locomotion in water the swimmer is trying to perform a significant part of the
working movements within the range of AMF in the
elbow, shoulder, hip and knee joints, to create maximal torque at the appropriate instants.
Arm pull in the front and back crawl and butterfly
is a complex movement. It consists of two parts: (i)
pulling—consecutive flexing of the arm at the wrist
and elbow joints and extension at the shoulder joint;
and (ii) pushing, performed by continuous extension at the shoulder joint accompanied by extension
at the elbow and wrist joints. Each part has its own
zone of AMF. The two largest pulses of the RF during arm pull (Fig. 10.12) are the result of the consecutive utilization of the AMF and highly precise
timing of joint movement in three joints. Swimmers
increase and decrease hand and forearm velocity
with every change of pulling direction. Correspondingly, intracyclic propulsive force changes in
pulses. The first largest peak of muscle effort occurs
during the pulling part of underwater movement
when the angle between the forearm and the direction of motion is about 45°, and the angle between
the forearm and shoulder is approximately 160°.
The final part of the pulling phase and first half of
the push phase is performed by active extension of
the shoulder with utilization of the hand and forearm as a supporting surface. Shoulder extension
gradually slows during the latter half of the push
phase, and active extension of the elbow take place.
The second largest pulse of RF occurs during the last
third of the push.
Maintaining uniform high intracyclic
swimming velocity
Swimming is a cyclical locomotion during which
the working phases alternate with preliminary
movements needed to recover the initial working
posture of the limbs. During the recovery phase
propulsive forces do not act on the swimmer’s body
and it is the subject of hydrodynamic drag and
inertia. Hence the swimming velocity decreases
until the working phase of the next swimming cycle
begins, when it starts to increase again.
Fluctuations of intracyclic swimming velocity are
inevitable since a significant part of pulling action is
performed beyond the range of AMF and recovery
is necessary. The fluctuations necessitate additional
effort to accelerate the body’s GCM and overcome
the inertia of the body and added mass of the water
(Issurin 1977). Thus velocity fluctuations increase
the energy cost of swimming.
The magnitude of intracyclic velocity fluctuations
may be reduced and average swimming velocity
increased by shortening the duration of recovery,
increasing the amplitude and frequency of the
pulling actions, and improving the timing of arm
and leg movements.
Reduction of hydrodynamic resistance and action
of negative forces
The position of the head relative to the water level
propulsive forces in swimming
and the horizontal alignment of the body affect
the magnitude of frontal resistance (wave-making
resistance + form resistance) experienced by the
swimmer. The swimmer should maintain the most
streamlined position and keep the angle of attack
within a given range.
When a swimmer adopts a prone, streamlined
position in the water the gravity force is balanced by
the upthrust (buoyancy force). During active swimming he/she needs to periodically lift the head and
part of the upper body to perform recovery and
inhalation. During these auxiliary movements the
weight of the ‘out of the water’ body parts may
increase from 5 to 15 kg, giving rise to the sinking force. To compensate for this sinking force
the swimmer must apply an additional upwardly
directed force. Skilled swimmers usually perform
the recovery and auxiliary movements rapidly with
minimal lifting of body parts out of the water. The
timing of arm and leg movements as well as transverse arm movements during the pull is partly
designed to compensate or eliminate the negative
action of this sinking force.
Optimal ratio of stroke rate to stroke distance
The stroke rate is the number of strokes or complete
swimming cycles performed per unit time (usually
per second). Stroke distance is the distance covered
by a swimmer per stroke or per complete swimming
cycle. Swimming velocity usually equates to the
product of stroke rate and stroke distance:
V = SR × SD
(10.8)
where SR = stroke rate (pulls · s–1) , and SD = stroke
distance (m).
It follows from Eqn. 10.8 that different ratios of SR
and SD may result in the same swimming velocity,
although an individual swimmer achieves a maximal
swimming velocity only at one particular ratio of SR
and SD. Too high a stroke rate disturbs the coordination of the swimming movements since the
muscles are not able to relax during recovery and
thus fatigue sets in very rapidly. During swimming
with a low SR and high SD the swimmer has to
make an excessive effort in every stroke, which
may increase the anaerobic fraction of total energy
229
supply. The consequent accumulation of lactic acid
decreases the swimmer’s working capability.
During training every swimmer selects the most
effective individual ratio of SR and SD. The ‘comfortable’ stroke rate seems to be the most stable
individual characteristic, depending probably on
the nature of the individual’s nervous system and
muscle fibre composition. It changes very little
over multiyear training periods. The objective of
technical training is to develop maximal SD for a
given individual’s comfortable stroke rate.
The value of stroke distance and its dynamics
during competitive racing are the important criteria of stroke quality. It depends upon technical
and physical training (muscle power) and an individual’s ‘feeling for the water’.
Conservation of mechanical energy within the
system of swimmer’s movements
Efficient conservation of kinetic energy within the
swimming cycle is achieved by the following.
1 Relatively rigid fixation of segments in joints during pulling actions (e.g. fixation of the shoulder at
the beginning of the downsweep) altered by fixation
of the hand and forearm in the elbow and wrist
joints at the end of insweep-beginning of outsweep).
2 Locomotor reconfiguration of the body in order
to store elastic energy, dampen oscillations of propulsive force, and reduce HDR via:
(a) optimal level of tension of body muscles
creating a relatively rigid frame on which are
transmitted the forces of hydrodynamic reaction
developed by the arm and leg movements;
(b) relaxation of non-active muscles; and
(c) kinematic streamlining—ideal alignment of
the body at the instants of peak propulsive force.
3 Use of the kinetic energy (inertia) of the recovering segments to increase propulsive momentum.
4 Transfer of the kinetic energy of the moving segments into potential energy of elastic deformation of
muscles and tendons.
Acknowledgement
The authors are grateful to P. Brown for help in editing the manuscript.
230
locomotion
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Chapter 11
Performance-Determining Factors in Speed Skating
J.J. DE KONING AND G.J. van INGEN SCHENAU*
Introduction
Speed skating can be described by an energy flow
model. Such a model includes expressions that describe both the generation of mechanical energy from
chemical substrates and the destination of the flow
of energy. These models are useful for the quantitative evaluation of the influence of technical, physiological and environmental variables on speed
skating performance. The objective of this chapter is
to explain the peculiar nature of speed skating technique and to demonstrate the effects of several performance-determining factors for speed skating by
means of a model based on the flow of energy.
Speed skating technique
In most patterns of locomotion, humans generate
propulsive forces by pushing against the environment in a direction opposite to the direction of
movement. A runner, for example, pushes backwards against a fixed location on the ground to propel himself in a forward direction (Fig. 11.1a). Even
in cycling, where it looks as if there is no rigid contact with the ground, forces are directed via the tyre
to fixed locations on the road. In speed skating,
however, something essentially different occurs.
Due to the peculiar qualities of ice, skaters are able
to glide with relatively high velocities in the desired
forward direction. Skaters make use of the so-called
*Prof. G.J. van Ingen Schenau passed away on 2nd April
1998.
232
‘gliding technique’, which means that the propulsive movements against the ice are made while
the skate continues to glide forward (van Ingen
Schenau et al. 1987; de Koning et al. 1995). However,
when a skate is gliding forward, it is impossible for
it to generate propulsive forces by pushing in a
backward direction. The only possible direction for
an effective pushoff is at right angles relative to
the gliding motion of the skate (Fig. 11.1b). The
difficulty of the skating technique lies in the transformation of the sideward pushes into a forward
velocity. This transformation can best be explained
by reference to Fig. 11.1b and Fig. 11.2.
The pushoff force (Fp) generated by the skater
has a horizontal (Fx) and a vertical component
(Fz). The magnitudes of these components depend
on the angle between the force vector Fp and the
horizontal, the so-called pushoff angle, α. The
horizontal component Fx of the pushoff force causes
acceleration in a direction perpendicular to the gliding skate, from right to left, or with a push from the
other leg, from left to right. The resulting sideward
velocity (v2 in Fig. 11.2) can be added to the gliding
velocity (v1) in a more or less forward direction.
These two velocities result in a new velocity (v3)
with a slightly changed direction in, again, a more
or less forward direction. When this is done alternately by the right and left leg, the skater makes a
sinusoidal motion.
During the skating cycle the trunk must be kept
almost horizontal to minimize frontal area and
hence air frictional losses (van Ingen Schenau 1982).
At the same time, on conventional skates, powerful
plantarflexion needs to be suppressed to prevent
performance in speed skating
233
z
Fp
Fz
Fp
Fig. 11.1 There are big differences
between running and skating in the
way in which propulsive forces are
generated. This largely explains the
differences in speed attained by these
forms of locomotion. (Adapted from
Gemser et al. 1999.)
v3
x
α
Fx
(a)
(b)
Ice track
direction
Gliding
direction
v2
v1
v3
v1
Track of the
skate
v2
Path of the centre
of body mass
Fig. 11.2 The pushoff results in a velocity (v2) of the
body’s centre of mass with respect to the skate. Together
with v1 this determines the new magnitude and direction
of velocity (v3) of the body’s centre of mass. (Adapted
from Gemser et al. 1999.)
y
the front of the blade from scratching the ice and
causing ice frictional losses and disturbances in
balance. The absence of trunk rotation and foot
rotation results in a pushoff which is mainly done
by rotation of only the upper and lower leg. This
means that for a proper gliding technique on conventional skates, the pushoff is mainly caused by
knee extension.
During the gliding phase of the skating cycle the
knee angle is more or less constant. During the
pushoff a rapid knee extension occurs. A closer look
at the knee angle during the pushoff shows that the
knee is not fully extended when the skate is lifted
from the ice (Fig. 11.3). This happens at a knee angle
of 160°. This early termination of the pushoff is
caused by the above-mentioned absence of trunk
extension and plantarflexion (van Ingen Schenau et
al. 1996). Due to this absence the acceleration of the
heavy trunk relative to the gliding pushoff skate
depends mainly on the velocity at which the hip
moves away from the ankle (pushoff velocity Vha in
Fig. 11.3). The peak in this velocity is reached far
before full extension, at a knee angle of 140°. Soon
after the instant that the velocity Vha reaches its
maximum, the inertia of the relatively heavy trunk
and contralateral leg pulls the skate from the ice and
brings the pushoff to an end. With instrumented
conventional skates we were able to measure
pushoff forces as well as ice friction forces during
skating. From the force signals we learnt that the
234
locomotion
output of the athlete. Recently all international-level
speed skaters have changed to these new skates. All
participants of the speed skating disciplines at the
1998 Winter Olympics in Nagano were using these
skates, resulting in new world records at each
skated distance. The introduction of this new skate
by the late Gerrit Jan van Ingen Schenau has changed
competitive speed skating forever. The results of
biomechanical and physiological research into the
exact mechanism behind the increase in performance achieved with this skate will be published soon
(Houdijk et al. in preparation).
Push-off velocity, Vha
(m· s–1)
Knee angle
(degrees)
180
140
100
2
1.6
1.2
0.8
0.4
160
Power in speed skating
140
Push-off force
(% body weight)
120
100
80
60
40
20
0
–0.8
–0.6
–0.4
–0.2
Time (s)
0
0.2
Fig. 11.3 The knee angle, pushoff velocity (Vha) and
pushoff force while skating on conventional skates. These
are averaged values, measured in five elite speed skaters.
In the last 0.2 s of the skating stride the pushoff takes
place. (Adapted from Gemser et al. 1999.)
peak in pushoff force is reached at a knee angle of
130°. The maximal force was equivalent to 150%
of body weight and dropped sharply when the
pushoff velocity was over its maximum (Fig. 11.3).
On the basis of the observations described above
and a comparison with results from experiments on
vertical jumping (Bobbert & van Ingen Schenau
1988), our research group constructed in the mid1980s a skate which permits the shoe to rotate in a
hinge relative to the blade of the skate (van Ingen
Schenau et al. 1996). We called this skate the ‘klapskate’. The skate allows for a plantarflexion without
the drawbacks described before. Skating with this
type of skate results in an increase in average power
Performance in speed skating depends strongly on
the power production capacity of the skater. This
power is primarily used to overcome the air and ice
friction and to increase the kinetic energy of the
skater. When a skater is skating at a constant velocity, there is no change in kinetic energy, so power
produced is equal to power dissipated by air and ice
friction. In such a particular case there is a balance
between power production and power dissipation.
In competition such situations are rare. In most
cases the generation of mechanical power by the
aerobic and anaerobic energy systems will not equal
the power necessary to overcome air and ice friction. When the energy systems are producing more
mechanical power than is required to overcome air
and ice friction the skater will accelerate, and when
the energy produced is less than required the skater
will decelerate. This will result in a certain velocity
profile over the course of the race. With the help of
models incorporating power production and power
dissipation, it is possible to simulate a race and predict the velocity profile and performance time. This
approach was used by van Ingen Schenau et al.
(1990, 1991, 1992, 1994), de Koning et al. (1992a) and
de Koning and van Ingen Schenau (1994) to simulate performances in speed skating, running and
cycling.
A model based on the described power equation
can be used to investigate the relative importance
of factors such as energy production and skating
posture and so guide training. For instance, it would
be interesting to know how speed skating perfor-
performance in speed skating
mance is influenced by training-induced changes in
physical parameters, such as oxygen consumption
and anaerobic capacity, and by technical parameters,
such as trunk position and knee angle. From previous studies it is known that factors like skating
posture and distribution of power during the race
have a strong effect on performance. Besides the
athletic ability of the skaters, environmental factors
such as wind (van Ingen Schenau 1982) and ice conditions (de Koning et al. 1992b) also strongly affect
performance.
The remaining part of this chapter will focus on
the use of a power equation applied to speed skating as a tool to demonstrate the relative influence
of several performance-determining factors. An
experimental analysis of technical and physiological variables was carried out and calculations
were made to predict the influence of each variable of interest on performance in the 500, 1000 and
1500 m races of particular skaters. The predicted
performances were compared with actual performances of the skaters during their national championships. The variables of interest were the aerobic
energy production, anaerobic energy production,
race strategy, skating position and environmental
factors.
Modelling of speed skating
Power equation
A model (van Ingen Schenau et al. 1990) for speed
skating based on a power equation that includes
expressions for power production and expressions
for power dissipation can be written as:
Po = Pf +
dEmcb
dt
(11.1)
where Po is the average total power output (the
mean generated power) of the skater, Pf is the average power loss to air and ice friction, and dEmcb/dt
is the average rate of change of the kinetic, rotational
and potential energy of the body. The rate of change
of mechanical energy of the body averaged over
multiple cycles is in speed skating predominantly
determined by the rate of change of kinetic energy
of the mass centre:
dEmcb d(1/2 mv 2 )
dv
=
= mv
dt
dt
dt
235
(11.2)
with v the cycle averaged speed. The rate of change
of kinetic energy can thus be calculated by:
Po − Pf =
d(1/2 mv 2 )
dt
(11.3)
To perform valid simulations of speed skating performance it is necessary to have valid expressions
for Po and Pf .
Determination of power production (Po)
The metabolic power production of the athlete is
the sum of the power produced by the aerobic and
anaerobic energy production systems. At the beginning of a maximal exercise bout, the external power
output can be considerably higher than that which
can be generated later during the exercise. This is
due to the immediate availability of energy-rich
phosphates and anaerobic glycolysis for the generation of muscle power output (e.g. Åstrand & Rodahl
1986; Serresse et al. 1988; Davies & Sandstrom 1989).
Due to the limited phosphate pool, the time taken
for the aerobic system to develop maximal aerobic
power, and the lower maximum value of this aerobic power, a large decrease in power output can
be observed during the course of maximally performed exercises.
To model aerobic and anaerobic power production as a function of time, we had 12 male speed
skaters, all participants of the Calgary Olympic
Oval Program, perform two cycle ergometer tests
on a mechanically braked ergometer: a 30 s all-out
sprint test and a 2.5 min supramaximal test according to a protocol by de Koning et al. (1994).
The 30 s sprint test was a Wingate-type test which
the subjects had to perform in an all-out fashion
right from the start. The 2.5 min test was preceded
by 6 min of submaximal cycling directly followed
by the 2.5 min test period. The subjects had to perform the test at an intensity higher than their maximal level, which was predicted on the basis of body
mass and power output values in a comparable
population of skaters (van Ingen Schenau et al. 1988;
de Koning et al. 1994).
locomotion
The mechanical power output was determined
by the product of the measured pedalling rate and
the measured braking force on the flywheel of the
ergometer. The results where corrected for the
energy flow to and from the flywheel of the cycle
ergometer.
The total metabolic power output during the
cycle ergometer tests has an aerobic (Paer) and an
anaerobic (Pan) component:
Po = Pan + Paer
20
16
14
12
10
8
6
4
(11.4)
2
For the estimation of the aerobic power the kinetics
of the oxygen consumption (Bo2) was modelled
with:
0
Bo2 = Bo2-max
(1 − e −λt)
(11.5)
with λ a time constant. On the assumption that 1
litre of O2 consumed liberates 20.9 kJ of metabolic
energy (Åstrand & Rodahl 1986) and with the gross
efficiency calculated from the power output and
oxygen consumption measured during the submaximal exercise preceding the 2.5 min test, the
mechanical aerobic power kinetics was modelled as:
Paer = Paer-max (1 − e −λt)
(11.6)
with Paer-max the maximal mechanical aerobic power
contribution. The value for the time constant λ
(0.1069 s–1) was obtained from literature (de Koning
et al. in preparation).
To determine the mechanical equivalent of the
anaerobic part of the total mechanical power measured during the 30 s sprint test, the aerobic contribution in the total mechanical power output was
subtracted from the total mechanical power:
Pan = Po − Paer
(11.7)
The resulting anaerobic power could properly be
described by a first-order system:
Pan = Pan-max e −γ t
(11.8)
with Pan-max the maximal mechanical anaerobic
power at t = 0 and γ a time constant. Values for Pan-max
and γ were obtained by fitting Eqn. 11.8 to Eqn. 11.7.
The expression for the anaerobic power output is
extrapolated to calculate the total power output
during the speed skating races (Fig. 11.4).
Anaerobic power
Aerobic power
Total power
18
Power (W)
236
20
40
60
80
100
120
Time (s)
Fig. 11.4 Aerobic and anaerobic energy kinetics during
high-intensity exercise. (Adapted from Gemser et al. 1999.)
As extensively discussed for running, the stroke
(or cycle) averaged value for the rate of change of
segmental energy in cyclic movements is equal to
the rate of change of mechanical energy of the mass
centre of the body only (e.g. Williams & Cavanagh
1983; Aleshinsky 1986a,b). The amount of power
associated with the acceleration and deceleration of
body segments is thus not accounted for in the
power equation. In comparison to cycling the power
associated with acceleration and deceleration of
body segments will be substantial in speed skating
(de Boer et al. 1986). This means that Po will be
smaller during skating than the mechanical power
actually liberated in the contracting muscles. It is
known from previous work that external mechanical power and oxygen consumption during maximal skating are lower than during maximal cycling
(van Ingen Schenau & de Groot 1983). It is assumed
that the difference in Po during cycling and skating
can be approximated by one parameter expressing a
certain (constant) fraction fr of the measured external power in cycling. The value of this parameter, fr,
is estimated on the basis of actual 1500 m performances. The 1500 m event is often judged as a key
distance in all-round speed skating since performance at this distance strongly relies on both the
aerobic and anaerobic pathways in power production. The parameter fr is defined as:
performance in speed skating
fr =
W1500 m
E1500 m
(11.9)
with W1500 m the sum of the kinetic energy and the
calculated work done against friction during the
1500 m race, and E1500 m the available mechanical
energy equivalent of the metabolic processes, as
measured on the cycle ergometer, during the time of
a 1500 m race.
To determine fr, the velocity and duration of the
1500 m skating performance were obtained from
the seasonal best times of the skaters in this study.
W1500 m was calculated with the equations for air
and ice friction. The available mechanical energy
equivalent of the metabolic processes (E1500 m) was
determined by integration of the equations for the
anaerobic and aerobic energy kinetics, as measured
during cycling, over the time needed to cover the
1500 m.
The total power output (Po) during speed skating
is now described by:
Po = fr(Pan + Paer)
(11.10)
It should be noted that fr is the only parameter that is
estimated from actual speed skating performances
of the athletes. Moreover, fr does not influence the
time constants and thus the kinetics of the aerobic
and anaerobic pathways.
Determination of power dissipated to friction (Pf)
In speed skating the skater has to overcome ice- and
air-frictional forces. Air friction has two components, friction drag and pressure drag. Friction drag
is caused by friction in the layers of air along the
body and is dependent on, for example, the roughness of the suit. In speed skating, friction drag
is relatively small with respect to pressure drag.
According to Bernoulli’s law, the pressure in the
front of the skater is higher than the pressure behind the skater. This is a result of a difference in the
relative velocity of the air with respect to the front
and back the body. This pressure difference is
mainly determined by the dynamic pressure 1/2ρv2
where ρ is the density of the air and v the velocity
of the air with respect to the body. Given a crosssectional area (the surface within the contour of a
237
frontal picture) Ap , the pressure drag equals 1/2ρv2Ap.
This relationship, however, does not account for the
influence of streamlining, and the contribution of
friction drag. Therefore, a dimensionless coefficient
Cd is added to this equation and is called the drag
coefficient. This drag coefficient can only be determined experimentally. Total air friction force Fair
thus equals:
Fair = 1/2ρv2ApCd
(11.11)
Wind tunnel experiments on speed skaters (van
Ingen Schenau 1982) showed a strong dependency
of Cd on velocity, v. With these wind-tunnel experiments relations between air friction and anthropometric variables as well as skating position were
made. For a steady speed v the air frictional force
(Fair) and air frictional power (Pair) has been modelled as:
Fair = k1e −0.000125h v12 l3 mF(θ 1 )G(θ 0 )H (v1 )
(11.12)
Pair = Fair v
(11.13)
with k1 = constant; h = altitude; v1 = velocity of the air
relative to the skater; l = body height; m = body
mass; F(θ1) and G(θ0) = expressions which account
for trunk position and knee angle, respectively; H(v)
= influence of the velocity on the drag coefficient;
and v = velocity of the skater relative to the ice. Since
velocity variations within a stroke are small in
speed skating, the influence of these within-stroke
variations in v on the calculation of Pair (and Pice) is
ignored.
The ice frictional force (Fice) and ice frictional
power loss (Pice) is assumed to be equal to:
Fice = µ mg
(11.14)
Pice = Fice v
(11.15)
with µ the ice friction coefficient and g the gravitational acceleration.
To obtain values associated with speed skating
techniques, the skaters were filmed during 1500 m
races at the Canada Cup and Olympic Oval Finale in
the indoor speed skating oval in Calgary. The subjects were filmed in the sagittal plane with a 16 mm
high-speed film camera operated at a frame rate
of 100 Hz. To define the positions of the lower
leg, upper leg and upper body, points on the body
238
locomotion
using the Runge–Kutta method. The simulations
were performed for the 500, 1000 and 1500 m events.
The input parameters for the simulation model
consist of subject-specific data, group averaged data
and data from the literature.
θ1
Factors that influence performance
θ0
Results from physiological testing and
film analysis
θ2
The primary purpose of collecting the anthropometric, physiological and movement analysis
data was to acquire parameter values for the simulation model described above. Table 11.1 shows
the mean values of the relevant test parameters.
Individual parameter values were used in the
model calculations.
θ3
Fig. 11.5 The most important angles for describing the
skating position. The common values for these angles
in all-round speed skaters are: θ1: 10 –30°; θ0: 100 –130°;
θ3: 60 – 80°. (Adapted from Gemser et al. 1999.)
corresponding with the lateral malleolus, knee joint,
greater trochanter and neck were digitized using
a motion analyser (Fig. 11.5). Each film frame was
digitized three times to improve the accuracy of
determination of the body segmental positions.
From these positions the average trunk angle (θ1)
and knee angle (θ0) during the gliding phase of the
stroke were obtained. These trunk and knee angles
were used to calculate the air frictional forces as
described above.
Simulations
For each step in the simulation, the rate of change of
kinetic energy was calculated with:
Po (t) − Pair (v) − Pice (v) =
d(1/2mv 2 )
dt
(11.16)
The time history of the kinetic energy of the mass
centre of the body, and therewith the velocity, was
acquired by simultaneous integration of this equation with a variable step size second-order predictor, third-order corrector integration algorithm
Simulation results
Typical examples of a velocity–time curve obtained
from simulation, time histories of power output and
frictional power losses are shown in Fig. 11.6.
According to the power equation described above,
the skating velocity increases as long as the power
output exceeds the power losses to friction. The
velocity decreases when these frictional losses are
larger than the power output.
The mean times necessary to cover the 500, 1000
and 1500 m derived by simulation are presented in
Table 11.2. The simulations appear to show a close
Table 11.1 Results from physiological testing and film
analysis.
Parameter*
Mean (SD)
BO2max (l · min−1)
Gross efficiency
Pan—max (W · kg−1)
γ (s-1)
Ratio skating/cycling fr
Length (m)
Mass (kg)
Trunk angle θ1
Knee angle θ0
4.57 (0.43)
0.21 (0.02)
17.83 (1.89)
0.0347 (0.008)
0.55 (0.06)
1.81 (0.02)
74.0 (4.4)
13.7° (4.1)
106.0° (5.5)
* For explanation of symbols see text.
performance in speed skating
15
Power production
15
10
Power losses
5
5
Velocity (m ·s–1)
Power (W ·kg–1)
Velocity
10
Power production
0
20
40
60
80
100
239
0
120
Time (s)
Fig. 11.6 Simulated pacing pattern of a 1500 m race.
The skating velocity increases as long as the power
output exceeds the power losses to friction. The velocity
decreases when these frictional losses are larger than the
power output. (Adapted from Gemser et al. 1999.)
Table 11.2 Mean results from simulations and actual
speed skating.
Distance
Speed skating*
Simulation*
Difference (%)
500 m
0:39.18 (1.33)
0:39.16 (1.32)
0.11 (3.13)
1000 m
1:18.08 (2.05)
1:16.30 (1.59)
2.33 (1.72)
1500 m
1:58.97 (2.04)
1:59.58 (1.92)
0.51 (0.22)
* ‘Stopwatch’ times, in minutes and seconds.
Values in ( ) denote standard deviation.
fit to the actual mean skating times. On average the
times derived from simulation are 1% different from
the actual times of the speed skaters in this study.
These results indicate that good predictions of
speed skating performances can be made with a
power equation model.
The good performance of the model gives us the
opportunity to carry out simulations in which we
systematically change different input variables of
the model. These changes in input variables will
give changes in simulated speed skating times and
hence demonstrate the relative importance of the
input variables on speed skating performance. In
the remaining part of this chapter we will focus on
variables that influence power production and variables that influence power losses to friction.
The energy for muscular contraction comes immediately from adenosine triphosphate (ATP). ATP is
split into adenosine diphosphate (ADP) and a free
phosphate group during the process of resetting the
myosin cross-bridge. There are three energy systems that counteract the decrease in ATP concentration during muscular contraction. They are the
phosphagens, the lactate-producing energy system
and the aerobic energy system.
The phosphagen energy system includes the ATP
within the muscle cell and a related compound, creatine phosphate (CP), which is capable of rapidly
converting ADP to ATP. The lactate-producing
energy system produces ATP at a high rate by
degrading glycogen to lactic acid. This system
works well except that lactate is an acid which
exerts several negative effects in the muscle cell.
The aerobic energy system produces ATP by oxidizing carbohydrates and free fatty acids (FFA).
This system depends upon the availability of
oxygen delivered from the circulatory system. In
most energy-demanding sports (running, cycling,
swimming, skiing) the aerobic energy system is of
primary importance. In speed skating, however, the
characteristic crouched posture and deeply bent
knee position interfere with blood flow to the leg
and hip muscles and increase the importance of the
lactate-producing energy system.
During high-intensity exercise, the oxygen
uptake increases rapidly to near maximal values
(Fig. 11.4). In contrast, the kinetics of the anaerobic
energy supply shows, after an initial peak at the
onset of exercise, a decrease as time progresses. The
decrease in anaerobic power output is larger than
the increase in aerobic power output, resulting in a
gradually decreasing total power output in time
(Fig. 11.4). The percentage aerobic vs. anaerobic
energy metabolism changes rapidly as the length of
the event increases. Table 11.3 presents the relative
contributions of the aerobic and anaerobic pathways to the total energy production per distance.
One should be careful when interpreting these
figures. The relative contributions include the large
amount of anaerobic work necessary to accelerate
during the start. When this part is covered, the
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locomotion
Table 11.3 Relative contribution in total work done by the
anaerobic and aerobic energy system.
Speed skating discipline
Energy system
500 m
1000 m
1500 m
Anaerobic
70%
49%
36%
Aerobic
30%
51%
64%
skaters will have to rely on aerobic power to a
greater extent than is suggested by the figures in
Table 11.3. Even at 1000 m one has to cover the last
lap predominantly on the basis of aerobic power.
During the last lap of a 1500 m race the energy
supply is > 90% aerobic.
Higher values for Bo2-max will only have small
effects on the relative contributions of the aerobic and
anaerobic energy systems at the different distances,
but considerable effect on skating speed, and thus on
final times. Table 11.4 presents the difference in speed
skating performance as a result of changes in Bo2-max.
The mean Bo2-max as measured during the cycle
ergometer tests is used as reference. The variation in
maximal oxygen uptake over which the simulations
are performed is close to the range in maximal oxygen uptake as found for the speed skaters. This
means that the variation in the maximal oxygen
uptake can be judged as a ‘physiological range’.
The same type of calculations can be done with
the anaerobic energy system. If we take the anaerobic capacity (the area under the anaerobic power
output curve, Fig. 11.4) as the variable to alter over
the range as observed in the group of athletes in this
Table 11.4 Effect of simulated changes in maximal
oxygen uptake (BO2-max) on performance time.*
Event
−10%
−5%
VO2-max
+5%
+10%
500 m
0:39.29
(+0.8%)
0:39.13
(+0.4%)
0:38.98
0:38.83
(−0.4%)
0:38.68
(−0.8%)
1000 m
1:17.31
(+1.5%)
1:16.71
(+0.7%)
1:16.15
1:15.60
(−0.7%)
1:15.07
(−1.4%)
1500 m
2:02.70
(+2.5%)
2:01.15
(+1.2%)
1:59.69
1:58.34
(−1.1%)
1:57.06
(−2.2%)
* ‘Stopwatch’ times, in minutes and seconds.
Table 11.5 Effect of simulated changes in anaerobic
capacity (Pan) on performance time.*
Event
−15%
−7.5%
Pan
+7.5%
+15%
500 m
0:41.03
(+5.3%)
0:39.97
(+2.5%)
0:38.98
0:38.07
(−2.3%)
0:37.24
(−4.5%)
1000 m
1:19.80
(+4.8%)
1:17.92
(+2.3%)
1:16.15
1:14.49
(−2.2%)
1:12.94
(−4.2%)
1500 m
2:04.56
(+4.1%)
2:02.08
(+2.0%)
1:59.69
1:57.44
(−1.9%)
1:55.32
(−3.6%)
* ‘Stopwatch’ times, in minutes and seconds.
study we see even larger effects on skating speed
(Table 11.5). This stresses the importance of the
anaerobic energy system for speed skating.
In most of the metric style speed skating events
there is a regularly observed tendency for the athlete to decelerate during the latter 30 –50% of the
event. In the longer events (5 km and 10 km), the
pace tends to be relatively more even, while some
contemporary athletes even have a ‘negative split’
(skating the second half faster than the first).
Tactical considerations aside, the primary issue
that determines the pacing strategy is, on the one
hand, the velocity of the skater when passing the
finish line (this velocity is useless after the finish
line, and thus represents a waste of kinetic energy)
and, on the other hand, the risk of a massive slowdown late in the race due to fatigue. In longer events
or in conditions with a greater potential for slowing
down if power output is decreasing (e.g. bad ice,
low altitude, windy conditions), a more conservative use of the athlete’s energetic resources is often
chosen. However, in shorter events or in events with
less potential for slowing down (e.g. high altitude,
good ice) the athlete and his or her coach often
choose a more aggressive strategy.
Performances in speed skating events depend on
the time taken to cover a certain distance. At the
start, it takes a considerable time to cover the first
few metres. This means that high acceleration at the
beginning of the race is beneficial. This is illustrated
by high coefficients of correlation between 100 m split
times and 500 m final times during major (sprint)
competitions. In a study during the 1988 Winter
performance in speed skating
Table 11.6 Results (race times*) from simulation with
three different strategies.
241
15
Strategy
500 m
1000 m
1500 m
1. ‘All-out’
0:38.98
1:16.15
1:59.69
2. ‘Super-sprint’
0:37.59
1:14.92
1:59.40
3. ‘Constant-power’
0:39.37
1:17.36
2:00.56
* ‘Stopwatch’ times, in minutes and seconds.
Velocity (m ·s–1)
Event
10
All-out strategy
Super-sprint strategy
Constant-power strategy
5
0
20
40
60
80
100
120
Time (s)
Olympics, velocity patterns of a large group of skaters
during starts in the 500 m event were obtained (de
Koning et al. 1989). The average acceleration in the
first second of the race, calculated from the increase
in velocity, showed a strong relation with the 100 m
and 500 m distance times. The coefficients of correlation between the average initial acceleration and
100 and 500 m times were –0.76 and –0.75, respectively. This means that a large part of the very small
range in final times of these highly trained Olympic
skaters could be explained by differences in acceleration during the first second of the start. Fast acceleration at the start of the sprint is only possible
when large amounts of anaerobic energy are available in the first few pushoffs of the race. This is supported by significant correlations between peak
anaerobic power output measured on cycle ergometers and personal best times in 500 m skating races.
With the simulation model some interesting calculations can be made to mimic different possible
strategies for pacing, and thus for spending the
available anaerobic energy during the race. When
we assume that a skater can spend a certain amount
of anaerobic energy (his anaerobic capacity) during
the race and he is free in the distribution of that
energy, different pacing strategies can be employed.
Three additional simulations were performed with
the following three strategies.
1 Strategy 1: the ‘all-out’ strategy, where the skater
was skating according to the anaerobic kinetics as
measured on the cycle ergometer.
2 Strategy 2: the ‘super-sprint’ strategy, where the
skater has a 20% increased anaerobic peak power
output but an unchanged anaerobic capacity.
Fig. 11.7 Pacing patterns during simulated 1500 m races
with an ‘all-out’ strategy, a ‘super-sprint’ strategy and a
‘constant-power’ strategy. (Adapted from Gemser et al.
1999.)
3 Strategy 3: the ‘constant-power’ strategy, where
the skater is producing a constant power output
after a 15 s ‘all-out’ start.
In all three simulations the energy spent during the
different races is equal. Results of these simulations
are summarized in Table 11.6.
The times in Table 11.6 show that the best results
are obtained when the power output at the onset
of the race is highest. These results show that the
anaerobic capacity in itself is not a decisive factor for
sprinting events. It rather appears that sprinting
performances are strongly influenced by the rate of
liberation of anaerobic energy at the very onset of a
race.
The results of the simulations of the 1500 m event
show that the most ‘sprinter-type’ strategy (strategy
2) only gives a small advantage. The strategy with a
constant power output after an all-out start of 15 s
is slower than the ‘all-out’ and ‘super-sprint’ strategies. The velocity patterns of the 1500 m skated
according to the different strategies are shown in
Fig. 11.7. The more uniform velocity pattern of the
‘constant-power’ strategy results in lower air frictional forces but has the disadvantage that the
skater is passing the finish with a high velocity and
thus a high content of kinetic energy. This kinetic
energy has its origin from the energy systems but is
not used to overcome friction, and in that sense is
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locomotion
useless. For best results there is an optimal distribution between energy used to overcome friction and
kinetic energy left at the end of the race. It should be
noted that for 1500 m races, strategies 1 and 2 could
create big problems for the athlete because of the
accumulated muscle lactate and associated reduction in power generation. Needless to say, this phenomenon is not incorporated in the simulations
given here. It is likely that during actual 1500 m
races skaters will make use of a combined strategy 1
and strategy 3 approach.
Power losses to friction
Coaches and scientists are well aware of the powerful impact that skating posture has on air friction.
All skaters are instructed to skate with a trunk position that is as horizontal as possible and with a knee
angle that, during the gliding phase, is as small as
possible. The effect on performance of a number of
these factors has been calculated, which gives an
indication of the magnitude of their influence. In
these calculations one single factor is varied at a
time, assuming that all other circumstances remain
the same. This is the only way in which an impression can be obtained of the relative importance of
such a factor. This does not mean that immediate
conclusions can be drawn regarding individual
skaters. For example, it will be shown that skating
just a few degrees lower will lead to a considerable
gain in time. But the posture of a skater cannot be
changed easily, since this has a major influence
on the force level at which, especially, the knee
extenders have to work. However, this kind of
knowledge does make clear that, besides technical reasons relating to pushoff, a deeper skating
posture is an important factor that should be
addressed during the development of a speed
skater. This example will hopefully sufficiently clarify what this section deals with, namely indicating
the relative importance of a number of factors that
influence friction and thus performance.
Some of these factors influence not only friction
but also the glide and pushoff techniques. Here also,
the focus in this section will be on the effects on friction and frictional losses.
skating posture
Figure 11.5 shows some important angles that
describe the skating posture. These angles are: (i)
the angle that records the position of the trunk with
respect to the horizontal (θ1); and (ii) the angle at the
knee joint during the gliding phase (θ0). This latter
angle is equal to the sum of θ2 and θ3 , which are the
angles that record the positions of the upper and
lower leg. The angles θ1 and θ0 have a big influence
on friction, and their influence on performance is
shown in Tables 11.7 and 11.8, respectively.
The results in Table 11.7 and Table 11.8 show that
the trunk angle especially is an extremely important
factor. One can state that skaters who have their
trunk in a relatively horizontal position have an
extremely large advantage compared to skaters
with a more inclined trunk position. With a trunk
angle only 5° smaller skaters are able to skate the
1500 m in 3 s less. When viewing recordings of
Table 11.7 Effect of simulated changes in trunk angle (θ1)
on performance time.*
Event
+5°
+2.5°
θ1 = 13.7° −2.5°
−5°
500 m 0:39.42
(+1.1%)
0:39.20 0:38.98
(+0.6%)
0:38.76 0:38.54
(−0.6%) (−1.1%)
1000 m 1:17.65
(+2.0%)
1:16.89
(+1.0%)
1:16.15
1:15.40 1:14.64
(−1.0%) (−2.0%)
1500 m 2:02.78
(+2.6%)
2:01.24
(+1.3%)
1:59.69
1:58.16 1:56.63
(−1.3%) (−2.6%)
* ‘Stopwatch’ times, in minutes and seconds.
Table 11.8 Effect of simulated changes in knee angle (θ0)
on performance time.*
Event
+10°
+5°
θ0 = 106°
−5°
−10°
500 m 0:39.50
(+1.3%)
0:39.24 0:38.98
(+0.7%)
0:38.72 0:38.47
(−0.7%) (−1.3%)
1000 m 1:17.88
(+2.3%)
1:17.01
(+1.1%)
1:16.15
1:15.28
(−1.1%)
1:14.40
(−2.3%)
1500 m 2:03.26
(+3.0%)
2:01.49
(+1.5%)
1:59.69
1:57.92
(−1.5%)
1:56.14
(−3.0%)
* ‘Stopwatch’ times, in minutes and seconds.
performance in speed skating
skaters in the 1960s and 1970s, it is clear that the
tremendous improvement in speed skating performances during the last decades is due largely to
an improvement in the trunk position. The same
recordings show that the current high-performance
speed skaters have smaller knee angles than the
skaters of former decades, but these differences are
not very large. This is understandable since the knee
angle in particular has a strong influence on the
force of the muscles that have to do external work.
This force level of the hip and knee extensor muscles
is to a large extent determined by the position of the
upper leg. Due to anatomical limitations, the skater
is not entirely free to choose each knee and trunk
position without changing the horizontal position
of his centre of gravity with respect to his ankle
joint. This might explain why, especially over short
distances, not all high-performance skaters can be
trained to hold their trunk in a horizontal position.
ice friction and altitude
The ice friction coefficient can vary greatly between
tournaments, but also during tournaments. The first
is not really disturbing. As long as all competitors
have good or bad ice the average times may exceed
expectations or be disappointing, but the ice conditions do not affect the competition. But when ice
quality changes during a tournament, a tournament
could very well turn into a lottery.
Measurements have shown that, especially on outdoor tracks, the ice friction coefficient may increase
by more than 50% between ice preparations. An ice
243
friction coefficient of 0.004 can be judged as good
ice; values in the range 0.005 – 0.006 indicate wet ice
or ice with frost on it, whereas values in the range
0.002– 0.003 indicate ice of superior quality. The
effect of a 50% increase in this coefficient on a 1500
m time would be 2.8 s. The final times for longer distance races (5 and 10 km) are even more sensitive
to such a change in ice quality (because the relative
contribution of ice friction is higher). Such influences
justify the use of the word ‘lottery’. The effect of ice
friction, expressed as the coefficient of ice friction,
on performance is shown in Table 11.9.
The air friction a skater is subjected to is directly
proportional to the density of the air, and air density
markedly decreases at higher altitudes. However,
air density can also vary notably at the same location. The air density is approximately proportional
to air pressure. The most extreme readings that can
be made from a barometer at sea level (970 –1040
millibar) could already account for a 7% difference
in air density. Expressed in terms of performance
time this means a maximal calculated difference of
approximately 0.8 s per lap as a result of changes in
air pressure alone. Of course, this holds true only
if all other circumstances remain equal, but this is
often not the case on outdoor tracks. High barometer readings are often coupled to fine and freezing
weather, while the advantage of low barometer
readings is often nullified by the concomitant
presence of wind and high humidity. Still, such
variations in air pressure will often be the prime
explanation for performances that are below expectations despite apparently optimal conditions.
Table 11.9 Effect of ice friction coefficient (µ) on performance time.*
Event
µ = 0.006
µ = 0.005
µ = 0.004
µ = 0.003
µ = 0.002
500 m
0:39.44
(+1.1%)
0:39.18
(+0.5%)
0:38.98
0:38.79
(−0.5%)
0:38.57
(−1.1%)
1000 m
1:17.60
(+1.8%)
1:16.80
(+0.9%)
1:16.15
1:15.44
(−0.9%)
1:14.76
(−1.8%)
1500 m
2:02.97
(+2.7%)
2:01.06
(+1.1%)
1:59.69
1:58.16
(−1.3%)
1:56.69
(−2.5%)
* ‘Stopwatch’ times, in minutes and seconds.
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locomotion
Table 11.10 Effect of (standardized) local barometric pressure on performance time.*
Event
+30 mB
+15 mB
P = 1010 mB
−15 mB
−30 mB
500 m
0:39.18
(+0.5%)
0:39.09
(+0.3%)
0:38.98
0:38.88
(−0.3%)
0:38.79
(−0.5%)
1000 m
1:16.80
(+0.9%)
1:16.47
(+0.4%)
1:16.15
1:15.81
(−0.4%)
1:15.48
(−0.9%)
1500 m
2:01.06
(+1.1%)
2:00.38
(+0.6%)
1:59.69
1:59.02
(−0.6%)
1:58.34
(−1.1%)
* ‘Stopwatch’ times, in minutes and seconds.
Table 11.11 Effect of altitude on performance time.*
Location (altitude above sea level)
Hamar
(126 m)
Nagano
(375 m)
Inzell
(690 m)
Calgary
(1035 m)
Salt Lake City
(1305 m)
Air pressure
0 m = 1000 mbar
984
954
917
879
849
500 m
0:39.70
(+1.8%)
0:39.49
(+1.3%)
0:39.25
(+0.7%)
0:38.98
0:38.81
(−0.4%)
1000 m
1:18.53
(+3.1%)
1:17.84
(+2.2%)
1:17.02
(+1.1%)
1:16.15
1:15.56
(−0.8%)
1500 m
2:04.41
(+3.9%)
2:03.05
(+2.8%)
2:01.43
(+1.5%)
1:59.69
1:58.55
(−1.0%)
* ‘Stopwatch’ times, in minutes and seconds.
The influence of air pressure is much more obvious on indoor tracks, but here too disappointing
times are often attributed to the ice conditions. For
example, when shortly after the opening of the
first 400 m indoor track in the world (Thialf in
Heerenveen, The Netherlands) many world records
were broken on that track while the air pressure was
(very) low. This led to unjustly high expectations
during later tournaments, simply because the air
pressure was not taken into account. Many skaters,
reporters and sometimes even coaches tend to
doubt the skills of the local ice resurfacers. By systematically measuring the air pressure, coaches
can assure themselves that the variable times in
Heerenveen are mostly due to changes in air pressure. During sprint tournaments, when the same
distances are skated on both days, even small differ-
ences in air pressure from one day to the next can
often account for small differences in average times.
As Table 11.10 shows, it is therefore always important to keep an eye on the barometer when judging
the performances on ice.
The air pressure and therefore the air density
decrease significantly at increasing altitudes above
sea level, as can be seen in Table 11.11. This means
that at high-altitude tracks, in principle, faster times
may be expected than at sea level. With the aid of the
simulations it has been calculated what the advantages of skating on higher-altitude tracks would be
at several distances if all other circumstances were
identical. The results are shown in Table 11.11,
where the altitude of Calgary is used as reference.
However, a number of marginal notes should be
made in this regard. First of all, the advantage of
performance in speed skating
decreased air resistance may be partly nullified by a
lower aerobic capacity, which is the result of the
decreased oxygen concentration in the air concomitant with decreased air pressure. This could result in
a lower oxygen consumption. Measurements have
shown, however, that, especially after a period of
acclimatization, the maximally generated power on
a cycle ergometer will hardly, if at all, decrease at
the altitudes which are mentioned in Table 11.11. In
addition, oxygen consumption is especially limited
on the muscular level in speed skating and thus the
influence of a decreased oxygen concentration in
the air will presumably affect performance at even
higher altitudes than it does in cycling or running.
Regarding this aspect one would expect faster
times, even at longer distances, if tracks were constructed at even higher altitudes.
A second aspect that should be considered when
interpreting the predictions of Table 11.11 is the previously mentioned effect of changes in air pressure
as a result of high- and low-pressure areas. If, for
example, one skates a personal best time in Hamar
or Heerenveen at relatively low pressure, a performance in Calgary can be really disappointing if
the race coincides with a high-pressure area. The
chances of this happening are rather high since the
average winter air pressure in Calgary, if converted
to sea level, is higher than in, for example, The
Netherlands or Norway. Therefore, the average
differences in performance between Calgary and
Heerenveen or Hamar are smaller than the model
predicts. This holds especially true for skaters who
245
often skate in Heerenveen or Hamar (they have a
higher chance of coming across low-pressure areas).
This unevenly distributed game of chance also
holds true for skaters who often skate in Calgary:
their performances in Hamar or Heerenveen can be
very disappointing in comparison with their own
personal best times.
Conclusions
From the issues that have been the focus of this chapter a number of conclusions can be drawn that may
be of great importance to speed skaters in competition.
As has been stated, the optimal performance of
the competitive skater depends on both the minimization of frictional losses and the maximization
of power. Regarding friction, the most important
factors are body position and air density. On the
power generation side it is clear that for short distances the distribution of available energy is of great
importance. Obviously, there must be caution in
translating simulation results for practical applications. Still, to summarize this chapter, it is possible
to create a picture of the mechanically ‘ideal speed
skater’ on the basis of this simulation approach. The
ideal skater skates low, keeps his or her trunk in
a good horizontal position, and generates a high
amount of power. This high power is generated predominantly by a large amount of work at pushoff.
The skater should use klapskates and pushoff correctly sideways, which theoretically makes every
pushoff optimally effective.
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cycling bouts. International Journal of
Sports Medicine 13, 447–451.
van Ingen Schenau, G.J., de Koning, J.J.
& de Groot, G. (1994) Optimisation of
sprinting performance in running,
cycling and speed skating. Sports
Medicine 17, 259–275.
van Ingen Schenau, G.J., de Groot, G.,
Schreurs, A.W., Meester, H. &
de Koning, J.J. (1996) A new skate
allowing powerful plantar flexions
improves performance. Medicine and
Science in Sports and Exercise 28,
531–535.
de Koning, J.J. & van Ingen Schenau, G.J.
(1994) On the estimation of mechanical
power in endurance sports. Sport Science
Reviews 3, 34–54.
de Koning, J.J., de Groot, G. & van Ingen
Schenau, G.J. (1989) Mechanical aspects
of the sprint start in Olympic speed
skating. International Journal of Sport
Biomechanics 5, 151–168.
de Koning, J.J., de Groot, G. & van Ingen
Schenau, G.J. (1992a) A power equation
for the sprint in speed skating. Journal of
Biomechanics 25, 573–580.
de Koning, J.J., de Groot, G. & van Ingen
Schenau, G.J. (1992b) Ice friction during
speed skating. Journal of Biomechanics 25,
565 –571.
de Koning, J.J., Bakker, F.C., de Groot, G.
& van Ingen Schenau, G.J. (1994)
Longitudinal development of young
talented speed skaters: physiological
and anthropometric aspects. Journal of
Applied Physiology 77, 2311–2317.
de Koning, J.J., Thomas, R., Berger, M.,
de Groot, G. & van Ingen Schenau, G.J.
(1995) The start in speed skating: from
running to gliding. Medicine and
Science in Sports and Exercise 27,
1703 –1708.
Serresse, O., Lortie, G., Bouchard, C. &
Boulay, M.R. (1988) Estimation of the
contribution of the various energy
systems during maximal work of short
duration. International Journal of Sports
Medicine 9, 456 – 460.
Williams, K.R. & Cavanagh, P.R. (1983) A
model for the calculation of mechanical
power during distance running. Journal
of Biomechanics 16, 115 –128.
Chapter 12
Cross-Country Skiing: Technique, Equipment and
Environmental Factors Affecting Performance
G.A. SMITH
Introduction
Relatively few sports have gone through revolutionary technique changes without abandoning
the old techniques. For example, in high-jumping,
the ‘Fosbury flop’ has completely displaced older
techniques. Virtually no one high-jumps with the
straddle or the western roll techniques any more.
In cross-country skiing, the revolutionary development of skating as a racing technique occurred in
the early 1980s. The performance advantages of skiskating became readily apparent within one or two
seasons, and by 1985 skating had come to dominate
elite ski racing. In an effort to salvage traditional skiing technique, the International Ski Federation (FIS)
decreed that World Cup events were to be divided
into ‘classic’ and ‘free technique’ races. Classic races
would be skating-restricted while the free technique
races were unrestricted. The half classic, half skating
split to the World Cup schedule which was suggested by the FIS has been maintained since then
and is matched by equal emphasis given to classical
and skating in national and even most regional ski
racing.
The ‘split personality’ of cross-country skiing
which has resulted from the maintenance of traditional and newer skating techniques provides a
wide variety of movement patterns which are commonly used in ski racing (see Fig. 12.1). The almost
infinite variations of technique that can be observed
in any ski race illustrate the daunting nature of
undertaking generalizations aimed at the relationship of technique to performance. Nevertheless,
cross-country skiing is a technical as well as an
endurance sport, where race performance is not
completely determined by physiology. Mechanical
factors clearly affect how skiers move over snow—
understanding those factors has challenged sport
biomechanists for several decades.
The development of biomechanical understanding of ski technique has followed a predictable
course from kinematics to kinetics. Early studies of
both classical (Dillman 1979; Martin 1979; Gagnon
1981; Dal Monte et al. 1983) and skating techniques
(Gervais & Wronko 1988; Smith et al. 1988) were
largely descriptive in nature and provided some
insights into the movement pattern characteristics.
Subsequent kinetic analyses have provided a starting point for explaining the observed kinematics,
though to date these explanations are quite incomplete. A review of this literature spanning more than
two decades encounters a large body of physiological and biomechanical writing devoted to understanding cross-country skiing performance. In that
somewhat confusing array of studies, one relationship has been clearer than most others: whether
skating or striding or double-poling, faster skiers
with better race performance tend to ski with
greater cycle length than do slower skiers (Bilodeau
et al. 1996). Figure 12.2 illustrates this relationship
for the double-poling technique with 20 skiers
competing in the women’s 30 km race from the
Lillehammer Winter Olympics. While this relationship has not been observed for all terrain and conditions, the frequency with which something like
Fig. 12.2 has been seen suggests that top-performing
ski racers are often able to glide further per cycle
than slower skiers.
247
248
locomotion
(a)
(b)
(c)
Fig. 12.1 Classic and skating techniques of cross-country skiing. Races are designated as ‘free technique’, in which skating
is permitted, and ‘classical’ in which it is restricted. Diagonal stride (a) is the fundamental classical technique, while
double-poling (b) is used in both disciplines. A variety of skating techniques (c) are used as terrain and conditions affect
ski glide characteristics.
12
forces acting on the system thus the focus of the
following will be largely on kinetic characteristics.
Cycle length vs. cycle velocity:
women's 30 km race
Cycle length (m)
11
Forces acting on the skier
10
9
8
r=0.81
7
6.0
6.2
6.4
6.6
6.8
7.0
7.2
Cycle velocity (m ·s–1)
Fig. 12.2 Cycle length and race performance. Doublepoling cycle length and race time data from the women’s
30 km race of the Lillehammer Winter Olympics (from
Smith et al. 1996). Faster skiers are often able to generate
greater cycle lengths than slower skiers while maintaining
similar cycle rates.
The remainder of this chapter will address factors which allow top-performing skiers to generate
greater cycle lengths than others. As a mechanical
system, a skier moving over snow is driven by the
Cross-country skiing performance is affected by a
wide range of factors that determine a skier’s speed.
Unlike an endurance sport such as running, where
physiological capacities are the major determinants
of performance, and where environmental conditions, equipment and technique have relatively
little effect, skiing performance is often influenced
by mechanics. Across the wide range of skiing
techniques, several general factors can be described which directly determine a skier’s motion.
These are illustrated in Fig. 12.3 and can be collectively grouped into forces which are resistive and
those which are propulsive in nature. This section
will describe various methods of force measurement, gravitational and inertial mass effects on skiing, and the origins of snow and air drag forces.
Following sections of this chapter will focus on minimization of drag forces acting against a skier and
on optimization of propulsive forces which drive
the motion.
factors affecting skiing performance
249
Gravity
Air drag
force
Poling
force
Ski drag
force
Fig. 12.3 Forces acting on a skier.
Reaction forces at the skis and poles
Skier-generated forces applied through the skis and
poles are probably the most easily adjusted of the
kinetic factors determining a skier’s performance. In
both classical and skating races, competitors commonly employ a variety of techniques which affect
the distribution of forces and the metabolic costs to
the skier (Hoffman 1992). Measurement of the ski
and pole reaction forces is of considerable interest
for understanding ski technique as it can shed light
on the relative importance of the upper body to the
legs in propulsion; it can illustrate characteristic differences between techniques; and it can be used to
detect individual skier weaknesses in technique.
Despite this potential, such force measurements are
rarely done and a rather incomplete picture of ski
and pole forces currently exists.
Undoubtedly, the difficulty of measuring ski and
pole forces in the natural environment has been a
major obstacle to advanced understanding of crosscountry skiing mechanics. Several research groups
have developed instrumentation and measurement
Reaction
force at
the ski
methods for obtaining skiing forces. In classical skiing, the skis are constrained to run in two parallel
tracks; the various classical techniques being relatively planar, they can be reasonably analysed using
two-dimensional methods (Ekstrom 1981; Komi
1985, 1987). In contrast, the more recently developed skating techniques involve three-dimensional
motion, which complicates the process of force
component determination (Smith 1989; Street &
Frederick 1995).
Two general approaches to ski force measurement have been used: the traditional force plate
embedded in a surface and portable force measurement systems attached to skis and poles. For skiing,
both approaches are difficult to implement and
involve serious obstacles to measurement without
adversely affecting technique and equipment characteristics. In classical skiing, several devices have
been used to measure ski and pole reaction forces.
For example, Komi (1987) reviewed both the fixed
and the portable plate approaches, showing his
current designs in 1987 (Fig. 12.4). Because of the
extended glide phases which characterize skiing
250
locomotion
Fz
Fy
+
7
8
9
–
+
10
11
12
13
14
15
Direction of
movement
16
1
2
3
4
5
6
1–6
7–12
13–16
Photocells
Mirrors
Force-plates
Fig. 12.4 Force plate with fixed positioning. This plate was designed for measuring pole and ski reaction forces in
diagonal stride technique and was mounted in a fixed position under snow. (From Komi 1987.)
strides, to measure a complete cycle requires an
unusually large force plate array compared with
other locomotion research. The 6 m-long plate created by the Finnish researchers was adequate for
slower skiing conditions, such as on uphill terrain,
where a full cycle with both right and left kick and
poling forces could be obtained (Fig. 12.5). The plate
was approximately 60 cm wide in the mediolateral
direction with four independent sections being separately measured. These allowed for independent
analysis of each ski and pole reaction force. Force
components in the vertical and anterior-posterior
propulsive direction were directly outputted from
the configuration and did not require additional
kinematic information.
In contrast, the skating techniques which became
popular in the succeeding decade are non-planar
three-dimensional movement patterns for which
the fixed force plate design would be inadequate.
Portable force plates attached to the ski when combined with telemetry equipment or with portable
data-logging computers allow the measurement of
ski reaction forces without the constraints imposed
by a fixed plate. Several examples of such portable
plates have been developed (Ekstrom 1981; Komi
1987; Smith 1989; Street & Frederick 1995) and have
been used for assessment of both classical striding
and skating techniques. However, the force components which can be obtained in this manner are local
to the coordinate system of each ski and pole rather
than the global system defined by the ski track. To
obtain meaningful force components requires the
additional measurement of ski and pole positions
and orientations synchronized with the force data
(Fig. 12.6). The three-dimensional motion analysis
required to obtain these kinematic data is a timeconsuming process which makes obtaining force
components for the skating techniques a considerably
factors affecting skiing performance
251
1/2 BW
0
Fz
Left pole
0
Fy
1/4 BW
0
1/1 BW
Fz
– +
270 ms
Right ski
Fig. 12.5 Pole and ski reaction forces.
Forces were measured using the force
plate array of Fig. 12.4 and have been
normalized to body weight (BW).
(From Komi 1987.)
0
Fy
+
1/4 BW
z
Vertical
force
x
Fig. 12.6 Force components in
skating. To obtain three-dimensional
force components in skating, the
resultant force applied normal to the
ski surface is resolved into a vertical,
a propulsive and a mediolateral
component. These are determined
from the ski orientation and edging
angles synchronized with resultant
reaction forces on the ski.
y
Resultant
ski force
Propulsive
force
Ski glide
direction
252
locomotion
more difficult undertaking than for the relatively
planar classical techniques. Later in this chapter results from the few studies which have reported skiing
force data will be discussed in the context of optimizing the propulsive forces from the skis and poles.
Sliding of skis on snow is a relatively complex physical phenomenon which is at best only partially
understood (Colbeck 1994b). In cross-country ski
racing, the snow surfaces are prepared mechanically with large grooming machines, which leave
a relatively smooth and firm surface behind. In classical races, parallel tracks are also set and used for
most portions of the course. Except when fresh
snow falls during races, skis generally glide on firm
surfaces into which they dig relatively little. The
efforts made in race course preparation are directly
aimed to reduce one aspect of ski drag forces—those
associated with a ski’s penetration into loose snow.
The energy lost to moving loose snow as a ski
ploughs through it slows ski glide. While this is a
recognized resistive force affecting ski performance,
little test information is available publicly (see Lind
& Sanders (1997) for general discussion). It is probably safe to assume that ski manufacturers expend
some efforts in understanding the specific characteristics which allow a ski to ride over soft snow
without much ploughing to reduce glide speed;
however, such studies are usually proprietary and
not readily available.
In contrast to the macroscopic forces involved in
ploughing through snow, several microscopic effects
which are thought to control the drag forces acting
on a sliding ski have been well researched and are
available in the general scientific literature. Several
characteristics of sliding surfaces affect the resistive
forces acting against a ski. These include the ski surface materials, the smoothness of the sliding surface
(‘structure’), the temperature of the snow and ski
surface, and electrical charge distribution on the ski.
Except in extremely cold conditions, ski sliding is
lubricated by meltwater from slight amounts of
heating of the surface. While generally serving to
decrease frictional forces for a ski sliding on snow,
in some situations excessive meltwater may increase
drag forces due to capillary action of the water,
0.16
Friction
Snow drag forces
0.20
µlub
0.12
0.08
µdry
0.04
µ
µcap
0
4
8
12
16
20
Film thickness (µm)
Fig. 12.7 Coefficient of friction (µ) and the effect of
meltwater film thickness. Total coefficient of friction is
influenced by dry friction, meltwater lubrication and
capillary drag. (From Colbeck 1992.)
snow crystals and ski base. Figure 12.7 illustrates
the relative contributions to the co-efficient of friction as a function of the amount of meltwater on a
sliding surface (Colbeck 1992). Under very wet conditions, capillary action may account for the largest
proportion of the drag force while under dry (cold)
conditions, limited melt-water lubrication affects the
frictional forces. Lind and Sanders (1997) include a
general discussion of these relationships; see Colbeck
(1992) for a more comprehensive analysis.
Snow and air temperatures have considerable
effects on the drag forces acting on a ski. A qualitative observation easily made while ski skating on
shaded snow and nearby sunny snow is the difference in drag force. Ski glide often can be dramatically decreased under cold conditions. These effects
are well known and have been addressed by ski wax
manufacturers whose products when matched to
snow conditions may decrease the snow drag forces
to some extent. Less well understood is how ski temperature influences drag forces and how it is affected
by base composition, ski design and environmental
conditions. Colbeck (1994a) instrumented skating
skis with an array of thermocouples along the base
and measured ski temperature during short periods
of ski-skating. Temperatures along the base showed
clear periodic oscillations corresponding to the skating cycle (Fig. 12.8). Local fluctuations of less than
1°C were typical during the glide and subsequent
recovery phases. Ski base temperature displayed a
factors affecting skiing performance
253
–8
TC
6
–9
Temperature (°C)
–10
5
4
–11
3
–12
Fig. 12.8 Ski base temperatures
during skating. Thermocouples (TC)
along the ski base responded to
frictional heating during each skating
stroke. During recovery while the
ski was in the air and off the snow
surface, the temperature dropped
to ambient levels. (From Colbeck
1994a.)
2
1
–13
–14
0
10
20
30
40
50
60
Time (s)
1.0
Voltage (V)
0.5
Fig. 12.9 Electrostatic charge on
skis during skating. As skis move
over snow charge build-up can be
detected as a voltage across the
top and bottom surfaces of the ski.
Electrostatic charge on the ski is
thought to attract dirt to the ski base,
which affects ski glide by increasing
snow drag forces. (From Colbeck
1995.)
0
–0.5
–1.0
–1.5
0
progressive increase from ski tip to tail and was
found to be sensitive to ski speed as well as environmental conditions (sun/shade and temperature).
Much is not understood about the relationship of
ski temperature to drag force. It is likely that surface waxing and structuring as well as overall ski
flexion characteristics affect surface temperature.
How these affect performance is unknown.
10
20
30
40
50
Time (s)
Ski drag is also thought to be affected by electrical
charging of ski surfaces. While the origins of such
charging are not clear, its magnitude can be measured directly by treating top and bottom surfaces of
a ski as a large capacitor. Colbeck (1995) described
this process with instrumented alpine skis; several
illustrations from that paper are relevant to crosscountry skiing. In Fig. 12.9, voltage fluctuations of
254
locomotion
3
Waxed
Voltage (V)
2
1
0
Unwaxed
–1
0
20
40
60
80
Time (s)
about ±1 V were found during skating. Discussion
in the popular skiing literature connects electrical
charging on skis to the pickup of dirt onto the sliding surface which in turn increases the snow drag
force (Brown 1989). Various ‘antistatic’ additives are
available as supplements to ski waxes. Figure 12.10,
from Colbeck (1995), compared an unwaxed alpine
ski base with an antistatic waxed surface and shows
how under some conditions such an additive may
be detrimental.
Air drag forces
Movement of a skier through the atmosphere
results in drag forces which are dependent on the
relative velocity of the skier and air. Except in the
case of strong tailwinds, such forces oppose a skier’s
motion. The well-known relationship from fluid
mechanics determines the magnitude of ‘profile’
drag forces which depend on air density (ρ), skier
frontal area (A), shape (CD, drag coefficient), and
relative velocity (V):
drag force = 1/2ρACDV2
(12.1)
This relationship emphasizes that two factors under
a skier’s control affect the air resistance opposing
motion: frontal area and shape. When skiing at slow
100
120
Fig. 12.10 Electrostatic charging
with different waxes. Some additives
to ski waxes are touted as being
‘antistatic’ supplements. In the
case illustrated here, the additive
increased rather than decreased
charge build-up on the ski. (From
Colbeck 1995.)
speeds such as on uphill terrain, air drag forces
are relatively small. But on downhill sections and
on fast snow, skiing speeds may easily reach 10–
20 m · s–1, where such forces may be substantial.
Skier adjustment of technique and body positioning
can reduce both the frontal area and drag coefficient.
Svensson (1994) included graphs illustrating the
variation of air drag force as a function of body position and speed (Fig. 12.11). On downhills, tucked vs.
upright body positions can reduce drag forces by
half or more; however, for the range of skating and
striding techniques, drag forces at a given speed differ by relatively small amounts. Other mechanical
and physiological factors probably affect technique
choice more than aerodynamics for the moderate
speeds typical of many parts of race courses.
While cross-country ski racing is an individual
sport, often skiers may be in a position to ski close
behind other competitors. In such circumstances, air
drag forces can be slightly reduced on the trailing
skier. The magnitude of the effect depends on the
skier speeds relative to the air and on how closely
the second skier is following. Bilodeau et al. (1994)
completed physiological measurements on leading and trailing skiers following closely behind. At
similar speeds, a skier ‘drafting’ behind a leader maintained heart rates about 5% lower than the leader.
factors affecting skiing performance
Air drag force vs. speed
upright and tuck
150
Upright
125
Force (N)
100
75
50
Tuck
25
0
2
4
6
8
10
12
14
16
18
20
22
Speed (m·s–1)
Fig. 12.11 Air drag force vs. speed for various skier
positions. Wind tunnel testing of skier positioning
showed that drag force is substantially different for
tucked positions in comparison to more upright postures.
(Data from Svensson 1994.)
Gravitational force and body mass
In hilly terrain, gravitational forces may be resistive or propulsive in direction. The magnitude of
the force depends on the slope involved and is
mathematically a function of the sine of the angle.
On downhills steeper than some minimum angle
(which depends on snow drag forces), a skier will
accelerate until reaching a terminal velocity where
gravitational force, ski/pole propulsive forces and
drag forces are in equilibrium. When simply gliding down such a hill, the equilibrium is reached
between gravity propelling the skier and snow and
air drag resisting the motion. Under fast snow conditions and on slopes where air drag is considerably
greater than snow drag this equilibrium is approximated by equating the gravitational force component with air drag force:
mg sinθ = 1/2 ρACDV2
(12.2)
where m is a skier’s mass, g is the acceleration of
gravity at the earth’s surface, and θ is the angle of
the downhill slope. This equation can be rearranged
to solve for velocity V. The equation includes both
mass and area terms which relate to a skier’s physical characteristics and allows some estimation of
the effect of body mass on terminal velocity. Because
255
body mass is mainly a function of volume, as body
mass increases, frontal area (A) also increases, but
not linearly with mass. Area changes approximately
as mass to the 2/3 power. Hence as body mass
increases, the ratio of body mass to frontal area does
not hold constant but increases. Terminal velocity
changes as the square root of the mass to area ratio
and thus increases with body mass. This wellknown result gives larger, more massive skiers an
advantage on downhill terrain.
On uphill terrain, drag forces are relatively small
and a skier’s mechanical work is mainly against
gravity. While more massive skiers must do more
work in hill climbing they also tend to have greater
metabolic capacities for work. Bergh (1987) has
argued that this balance of physical capacity vs.
work against gravity tips mainly in the favour of
larger skiers. On flat terrain and moderate uphills,
more massive skiers may have a slight advantage
over smaller skiers; on steep uphills, low mass is a
definite advantage. Hoffman et al. (1990) tested the
relationship of body mass to energy cost in roller
skiing. While they found the frictional characteristics of roller skiing to be slightly different than
skiing on snow, other relationships were reasonably matched to the theoretical predictions of Bergh
(1987). The advantages for skiers of large mass are
slight and the ranks of elite cross-country skiers
span a wide range of body sizes (Bergh & Forsberg
1992). Using data from Olympic races, Street and
Gregory (1994) have shown that despite a large
mass range for male competitors (58 – 85 kg), no
relationship of mass to 50 km race performance was
observed.
Minimizing drag forces
While skiing performance is influenced by all of the
kinetic factors discussed in the previous sections,
drag force acting on the skis is probably the focus of
more effort than the other forces affecting motion.
After training preparations are complete, skiers
have little control over kinetic factors affecting performance like air drag, body mass and snow surface
conditions. But considerable effort is put into ski preparation in hopes of minimizing the drag forces which
slow ski gliding. The magnitude of performance differences due to these forces is not well known.
256
locomotion
Ski glide speed and performance
Differences in glide characteristics between skis and
between ski base preparations are often detectable
by even casual recreational skiers. But at the elite
level of international competition, most teams
have professional technicians who specialize in
ski preparation and maintenance. Therefore, one
would expect to find relatively homogeneous glide
characteristics within such competitors. There are
numerous stories within the nordic skiing community about races where strong teams have been
handicapped by poor choices of wax and ski preparation for difficult conditions. But excluding these
unusual situations, many skiers suspect that glide
characteristics remain a distinguishing advantage
of the very fastest skiers. In a study designed to test
this assumption and carried out during the 1992
Winter Olympic Games at Albertville, glide speed
measurements were recorded during the men’s
50 km race (Street & Gregory 1994).
The 50 km race at the 1992 Olympics involved
three laps of about 17 km. Near the 15 km point
(32 km at the second lap), a moderately steep downhill of about 150 m length descended to a flat of
about 40 m. The downhill was of sufficient length
that skiers approached terminal velocity for that slope
and conditions. All descended using a tight, tucked
position. Video records were made of the skiers
gliding through the flat region after the hill during
the first and second laps and their velocities through
a 20 m mid-section on the flat were determined.
Glide speed on a downhill is affected by skier mass,
air drag, snow drag and the initial velocity at the top
of the hill and was distributed quite widely (Fig.
12.12). Street and Gregory systematically analysed
each factor through modelling of skier motion down
such a slope given the range of body sizes and initial
velocities at the top of the hill. Initial velocity and air
drag characteristics (A and CD) probably had relatively smaller influences on the variability of glide
speed observed at the bottom of the hill while skier
mass and snow drag were found to have considerably more influence on ultimate glide speed. However, mass of the skiers in the study was not related
to overall performance (r = 0.12), or to glide speeds
in lap 1 (r = 0.24) or lap 2 (r = 0.16). Hence, mass
explains very little of the variability of glide speed
observed in this race. The frictional forces of the ski
sliding over snow were probably the largest determinant of glide speed in this situation.
In a skating race such as the Olympic 50 km analysed by Street and Gregory (1994), glide characteristics of the ski affect every stride a skier takes
as the skating techniques involve pushing from
a moving ski. On fast downhills such as that analysed, snow drag and air drag forces both are
important, but on flats and uphills where speed is
considerably less, snow drag force is a dominant
factor. While it is more difficult to assess the influence of snow drag on performance in these slower
environments, it is likely that a substantial fraction
of race performance is explained by this factor. Of
course on uphill and flat terrain, physiology and
technique characteristics have considerable effects
on performance as well.
17
Glide speed (m·s–1)
16
15
14
13
12
7000
Lap 1
Lap 2
7500
8000
8500
Finish time (s)
9000
9500
Fig. 12.12 Glide speed vs. race time.
Top finishers in the men’s 50 km race
(Albertville Olympic Winter Games
1992) were faster through a test area
following a 150 m downhill. Snow
drag was found to account for much
of this relationship. Skier mass, initial
velocity and aerodynamic
characteristics had less effect on glide
speed variability across skiers. (Data
from Street & Gregory 1994.)
factors affecting skiing performance
Ski pressure distribution
The importance of glide to ski performance has
stimulated efforts to measure various characteristics
which affect snow drag forces. Of most importance
is probably a ski’s pressure distribution under
load (Brown 1989). Qualitatively, a match of snow
firmness, skier weight and ski stiffness must be
made so that the ski tip does not plough through the
snow (too stiff) or the mid-section of the ski does not
drag (too soft). A ski designed to optimize glide will
distribute the skier-applied forces in a smooth pattern without local fluctuations, which are thought to
increase drag. Unfortunately, other factors complicate ski design. Skating skis must also be stable and
track well and they must be torsionally stiff to allow
edging. Classical skis are designed primarily to
glide in tracks and must be capable of dramatically
different pressure distributions under varying loads.
A classical ski must be able to flex sufficiently to press
the mid-section firmly against the snow for wax grip-
257
ping yet glide smoothly on the tip and tail regions
when moderately loaded. Typical pressure distributions for skating and classic skis are illustrated in
Fig. 12.13. While the skating ski pressure distribution results in relatively low pressure mid-ski at full
body weight, the classic ski exhibits large mid-ski
pressures at full body weight (see Ekstrom 1981).
The pressure distributions illustrated in Fig. 12.13
show the general response of the example skis to
loading, and where available for individual skis this
may provide a useful means of matching skis with
skier. However, very little careful research is available in the public domain about how pressure distribution affects ski glide. Ski manufacturers may
have proprietary information detailing such relationships but little is available in the scientific literature. Further, the pressure distribution information
that is available (like Fig. 12.13) suffers from the
difficulty of generalizing to real skiing conditions.
Dynamic loading of skis, particularly when edged
as in skating, is likely to generate different pressure
Fischer RCS skating ski
Full
BW
Tail
Force transducers
at 10-cm intervals
Half Tip
BW
Fig. 12.13 Pressure distribution
under skating and classic skis.
Characteristic pressure distribution
patterns were measured for a range
of forces. At full body weight (BW)
classic skis must allow the ski
mid-section with grip wax to press
against the snow, while skating
skis under similar load distribute
the force quite differently.
(Adapted from pressure distribution
graphics from Eagle River Nordic:
www.ernordic.com/FischerRCSSkt.
htm and www.ernordic.com/
FischerRCSCapPlus.htm.)
Fischer RCS classic ski
Tail
Full
BW
Tip
Half
BW
Force transducers
at 10-cm intervals
258
locomotion
Top view
Skiing direction
Fz
Fx
Fy
100cm
100cm
Fy
Fx
Front view
A
B
C
Fz
Fx
Fy
Side view
Fz
distribution patterns than the flat, static loadings
typically measured. While portable instrumentation
for dynamic measurement of ski pressure has not
been currently developed, a fixed force plate design
described by Leppävuori et al. (1993) allows some
assessment of pressure distribution under a ski.
This unusual force plate (Fig. 12.14) was composed
of 20 beams of 10 cm width and more than a metre
length. Each was instrumented for measurement of
three-dimensional force components. The array of
beams was configured for placement under snow
Fig. 12.14 Force plate composed of
multiple instrumented beams. This
unusual design allowed not only
determination of three-dimensional
forces in skating but also the dynamic
force distribution under the ski
during a skating stroke. (From
Leppävuori et al. 1993.)
cover which allowed measurement of ski reaction
force components by summing the 20 beam outputs
(Fig. 12.15). Unfortunately, the overall length of the
plate (2.2 m) is not much longer than typical crosscountry skis, which during a single skating stroke
or single step in classical skiing may easily glide
through several metres. These limitations hinder
full stance phase ski reaction force measurement but
do provide some insights into force under regions of
the ski. Figure 12.16, from the paper by Leppävuori
et al., compares two force distributions during mid-
factors affecting skiing performance
Gliding phase
259
Kick phase
Final
kick phase
Initial
kick phase
1200
1000
Fig. 12.15 Ski reaction force in
skating. Due to the relatively short
force plate length, the ski was only
partially on the force plate as skating
began. Thus, the early phases of the
force–time record are much less than
observed with other measurement
systems. (From Leppävuori et al.
1993.)
Force (N)
800
b
a
600
400
ΣFz
ΣFx
200
0
–100
0.1
0
0.2
0.3
0.4
ΣFy
0.5
0.6
0.7
0.8
0.9
Time (s)
SF ski
250
Force (Fz) (N)
200
150
100
50
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
Beam number
*
*
4
5
*
*
7
8
T1 ski
*
*
250
Fig. 12.16 Force distribution underneath skis in skating. Two ski designs
were measured for force distribution
near the middle of the skating stroke.
The peak forces were located just
behind the heel of the boot. Note that
the pattern is quite different from the
static measurements of Fig. 12.12.
(From Leppävuori et al. 1993.)
Force (Fz)(N)
200
150
100
50
0
1
2
3
6
9 10 11 12 13 14 15 16 17 18 19 20
Beam number
260
locomotion
stance when ski loading is probably about body
weight. Both skis exhibit considerably different
patterns from that shown in Fig. 12.13, which was
measured statically. Whether this was due to a true
difference in dynamic vs. static loading of skis or if
it was due to skier technique or perhaps to some
instrumentation idiosyncrasy is unknown.
While we currently recognize that ski flex and
the pressure distribution pattern are probably very
important factors affecting ski glide, additional
instrumentation for dynamic measurement will
probably be required before the subtle relationships
between ski glide and ski design will be thoroughly
explored and understood.
Ski surfaces and friction
Snow drag forces result from a combination of
ploughing of a ski and of surface interactions with
snow. Ploughing is largely a function of ski stiffness
characteristics while surface friction depends on
ski base material, wax on the surface, roughness of
the surface, snow grain size, temperature, and other
physical conditions. Figure 12.7 (Colbeck 1992)
illustrates the coefficient of friction of a ski as a function of meltwater film thickness, which in turn
depends on various snow and ski characteristics. At
very low temperatures very little melting is thought
to occur as a ski slides over snow. The dry frictional
forces of low-temperature sliding tend to be quite
large. In Fig. 12.17a,b the direct interaction of snow
crystals and ski surface can be seen. Sliding under
such conditions requires either deformation or fracturing of the snow crystals (Colbeck 1994b). In
contrast (Fig. 12.17c), under warmer, wetter conditions where meltwater is created, sliding may be
accomplished with at least partial separation of
the ski surface from snow crystals. Whether some
direct ski to crystal interaction exists under these
conditions depends on how much meltwater is
generated, which depends on temperature and
frictional heating.
Polished hard slider,
old dry snow
(a)
Hard slider,
new dry snow
(b)
Soft slider, old snow,
liquid lubrication
(c)
Soft slider,
new dry snow
(d)
Fig. 12.17 Snow–ski surface interactions. Ski surfaces may be prepared with hard or soft waxes which will interact with
wet and dry snow in different ways. New dry snow tends to have small fine crystals which ‘catch’ in the small surface
roughnesses of the ski and wax. Older dry snow is more rounded and may produce less snow drag than newer snow. Wet
snow may have free water which creates drag on the ski through capillary action. (From Lind & Sanders 1997; Fig. 8.3.)
factors affecting skiing performance
Meltwater interaction between ski and snow crystals serves to lubricate sliding but also introduces
capillary drag, which has a magnitude dependent
on the contact angle of water with the ski surface
(Colbeck 1994b). Contact angle is affected by the
thin film of wax normally applied to ski surfaces.
Various wax compositions allow for the ‘tuning’ of
ski surface to the snow characteristics. These compositions range from relatively hard waxes, which
are generally used in cold conditions with little
meltwater generation, to quite soft waxes for wet
snow with considerable meltwater affecting sliding.
Wax hardness is thought to affect the penetration of
snow asperities into the wax, which in turn affects
melting. Too little penetration into a very hard wax
generates little heating of the surface and little meltwater generation. Too soft a wax may result in wax
deformation rather than snow crystal melting. In
addition to crystal penetration, wax composition
affects water contact angle. While it is generally
assumed that warmer glide waxes are in part composed to decrease contact angle, no published data
exist to support this expectation.
Ski wax chemistry is largely a proprietary science
hidden to the public. While the past decade has seen
the introduction of numerous fluorinated ‘waxes’
for skis, little has been published on the physical
processes which influence their sliding characteristics. Traditional waxes have been more thoroughly
explained chemically and physically (see Street &
Tsui 1986). Other additives to ski wax (such as
graphite) are touted as having antistatic characteristics. Sliding skis do generate small surface voltages
such as that shown in Figs 12.9 and 12.10 (Colbeck
1995). However, the extent to which such charge
build-up attracts dirt (Brown 1989) and how substantially it may affect ski glide is unknown.
Surface roughness characteristics (referred to as
structure) are also known to affect ski sliding over
snow. The effects involve complex interactions of
pore size between snow crystals, amount of meltwater and direction of the roughness elements
(Colbeck 1994b). Under warm conditions with
abundant water lubrication, the ski surface may
be separated by meltwater from the snow crystals.
With minimal separation, snow crystals may ‘catch’
in surface roughnesses, but with thick meltwater
261
layers, appropriately sized roughness is thought to
break up water droplet attachments between ski
and snow. At the same time, surface smoothness is
important as it enhances water slippage. The direction of surface roughness may also affect snow drag.
Colbeck (1994b) suggested that structure orientated along the ski is advantageous under wetter/
warmer conditions, while transverse orientated
structure may work better under colder conditions
when less melting occurs. Unfortunately, determining the effect of structure size and orientation under
various snow conditions is still a matter of experiment. While there are many coaching suggestions
for ski base preparation, these are largely based
on collective wisdom rather than systematic, controlled invest-igation aimed to advance theoretical
understanding.
Optimizing propulsive forces
Motion of a skier is determined by the sum of the
forces acting on the body (Fig. 12.3). While minimizing drag forces is an important component of
optimizing performance, it is skier-generated propulsive forces which directly cause forward motion.
These propulsive forces are one component of the
three-dimensional resultant reaction force at each
pole and each ski (Fig. 12.6). An earlier section of
this chapter reviewed some of the instrumentation
that has been developed for force measurement in
skiing. This section will focus on the components
of force and the factors affecting optimization of
propulsion.
Classic technique forces
The vertical and propulsive components of force
shown in Fig. 12.5 (Komi 1987) represent the relatively little that is known about diagonal stride
forces (see also Ekstrom 1981). This classic technique involves ‘kicking’ from a momentarily stationary ski onto the other gliding ski, which in the
next half cycle slows to a stop allowing the skier to
kick from it. During the very brief stationary period
of the ski’s motion, a large vertical force compresses the mid-section of the ski against the snow.
With appropriate wax on the ski, the mid-section
262
locomotion
momentarily sticks to the snow due to the large
normal force and high pressure in that region (Fig.
12.13). The static frictional force is large enough
during the kicking phase that a brief propulsive
component of force in the forward direction can
be generated. The magnitude of this force depends
on the frictional characteristics during kick. This
can vary widely depending on snow conditions,
ski stiffness and wax properties. While vertical
forces during this kick phase easily exceed body
weight, the propulsive forces are much smaller
(approxim-ately 10 –20% of body weight) and are
of very short duration—less than 0.1 s (Ekstrom
1981; Komi 1987). In contrast, skating forces (discussed below) are applied over a considerably
longer time interval.
Generating propulsive force during the kick
phase of diagonal stride requires careful timing of
the vertical and horizontal forces matched to the
glide speed of the ski. As the ski slows to a stop, the
large vertical force must quickly compress the cambered mid-section of the ski to the snow surface,
which momentarily creates a large static frictional
force. Optimal technique directs the ski reaction
force vector at an angle such that the propulsive
force component matches the maximum frictional
force attainable for the conditions. An early kicking
motion will compress the ski mid-section while the
ski is moving and tend to decrease the glide unnecessarily. A late kick will compress the ski camber
after the ski has momentarily stopped and will
decrease the vertical force component, which will in
turn decrease the static frictional force from which
propulsive force is generated.
In both classical and skating techniques, poling
forces are mainly axial in direction and have been
measured using both under-snow force plates and
instrumented poles. If instrumented poles are used,
the pole orientation in space can be used along with
the axial force to determine force components. In
classical ski techniques like diagonal stride and
double poling, the poles move mainly in a sagittal
plane and forces can be resolved into vertical and
propulsive components. For a given poling force,
the propulsive component increases as the pole is
angled in the forward direction and away from
vertical. Specifically, the vertical and propulsive
components are functions of the angle θ (with
respect to vertical):
propulsive component = Fpole sinθ
(12.3)
vertical component = Fpole cosθ
(12.4)
where Fpole is the resultant force along the longitudinal axis of the pole. Thus when the poles are vertical
(zero angle), no propulsive force is generated. As
poling angle from vertical increases, the proportion
of propulsive force increases. While vertical poling
forces do not contribute to propulsion, they may act
to decrease the vertical reaction forces on the ski(s)
and potentially diminish snow drag forces. (This
effect has not been measured and we can only
conjecture that the vertical poling forces would
decrease ski reaction forces by perhaps 20% of body
weight during the glide phase of diagonal stride.)
From the relationship of pole angle to propulsive
force component, a superficial assessment would
suggest that skiers should plant the pole at an angle
well beyond vertical to maximize propulsive force
throughout the poling phase. However, most elite
skiers do not follow this pattern. In a study of
double-poling technique, Smith et al. (1996) found
that under relatively fast conditions skiers planted
the poles at about 15° and that faster skiers tended to
plant the pole closer to vertical. Mechanically this
makes sense as it allows for a longer period of
poling—more vertically planted poles tend to be
planted further forwards and are in contact with the
snow for a longer time period. With this pattern, the
pole is initially relatively vertical as forces generated by elbow and shoulder extensor activity build
toward peak values. As poling progresses and the
poling angle becomes more effective, poling forces
peak. Later in the poling phase, as resultant forces
diminish, the pole angle continues to increase away
from the vertical enhancing the effectiveness of the
poling force. These effects can be seen in the Fy force
curve of Fig. 12.5, where a relatively sustained
plateau of propulsive force was observed.
A more vertically planted pole may also place the
arm in a more advantageous position for sustained
extension activity in a stretch–shortening cycle.
Figure 12.18 illustrates the elbow angle to pole angle
relationship for several top finishers in the women’s
factors affecting skiing performance
Elbow–pole angles during poling
263
Skating forces
160
Elbow angle (degrees)
150
140
130
#45
120
110
100
90
80
#39
70
#40
60
50
0
10
20
30
40
50
60
70
80
90
Pole angle (degrees)
Fig. 12.18 Elbow and pole angles during double-poling.
Beginning at the left of each curve, poling began with the
poles about 10–15° from vertical and proceeded to more
inclined poling positions. Elbow positionings varied
across subjects. Mean elbow angle at pole plant was about
106°; however, some, like skier #45 (the race winner), used
a considerably more extended elbow positioning initially.
Most skiers had considerable elbow flexion near the
beginning of poling, which probably involved preloading
of the triceps brachii prior to elbow extension. (From
Smith et al. 1996.)
30 km race at the Lillehammer Olympics (Smith et al.
1996). These (and most other) skiers of the study
planted the pole at about 10–15°. Initial arm motion
involved flexing of the elbow followed only later,
when the poles were inclined at 40 or 50° from vertical, by a rapid elbow extension. It is likely that some
preloading of triceps brachii muscles occurred early
in poling followed by elbow extension and active
muscle shortening later when pole angles were
most effective. From Fig. 12.18, it is apparent that a
somewhat more extended elbow position at pole
plant may allow for a longer period of preloading
with greater flexion preceding elbow extension at
pole angles greater than 45°. These assessments
are based on pole–arm–trunk kinematics in
double-poling. While it is likely that the segmental
relationships will be slightly different in diagonal
stride where trunk flexion is minimal, the principle
of planting the pole in a manner that enhances
preloading and takes advantage of the stretch–
shortening cycle for most effective poling angles
must still be advantageous.
Ski reaction forces in the skating techniques are orientated approximately perpendicular to the ski surface. Because skating skis are prepared with glide
wax and are without the grip waxes required for
classical skiing, there is no means of using static
friction to generate propulsive force. In a manner
similar to speed skating, the ski is set down at
an angle to the forward direction and while gliding
it is placed on edge. The edged platform of the ski
resists forces perpendicular to it as these simply
compress the snow under the ski. Forces in other
directions cannot be generated as the frictional
forces are insubstantial. Figure 12.6 illustrates the
resultant ski reaction force perpendicular to the
ski surface; components can be determined if the
ski positioning with respect to the snow surface
(edging angle) and with respect to the forward
direction are known.
While there are various ski reaction force patterns which characterize each of the skating techniques (Fig. 12.19), the generation of propulsive
force involves similar relationships in each case.
The propulsive force component from a skating ski
depends on the ski’s edging angle and on its orientation with respect to the forward direction. With the
resultant ski force (Fski) normal to the ski surface,
each of these angles affects the propulsive component as the sine of the angle. Thus propulsive force
component from a skating ski can be calculated from:
Fpropulsive = Fski sinα sinβ
(12.5)
where α is the edging angle of the ski surface with
respect to the snow surface (0° being flat) and β is
the orientation angle (0° being straight ahead). From
this equation it is obvious that propulsive force
increases (for a given resultant ski force) as either
the orientation angle or the edging angle increases.
A common observation in skating is the relationship of ski orientation angle to skiing speed. On flat
and fast terrain, the skis are angled away from the
forward direction a relatively small angle, while
under slower conditions and on uphill terrain the
ski angles increase substantially. For example, on
flat terrain used during the 1992 Olympic races, ski
angles were about 6 –8° (men; Smith & Heagy 1994)
264
locomotion
V2 skate force vs. time
1200
1250
1000
1000
800
Force (N)
Force (N)
V1 skate force vs. time
1500
750
600
500
400
250
200
0
0.25
0.50
0.75
1.00
1.25
Time (s)
0
0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
Time (s)
Fig. 12.19 Resultant ski reaction forces during skating. In skating, the resultant force is approximately perpendicular to
the ski surface. Subtle differences of timing exist for the various skating techniques (see Fig. 12.20). Each graph begins the
cycle at pole plant. V1 involves one poling action while V2 technique has two poling actions per cycle. Cycle times for V2
are typically longer than for V1.
and 10 –12° (women; Gregory et al. 1994). In contrast, skiers on uphill terrain of the Calgary Olympic
races skated with a much greater angle of skis to
the forward direction (means about 28–30°) (Smith
et al. 1988). Mechanically, this response would be
expected based on the relationship of ski angle to
propulsive force component expressed in Eqn. 12.5.
On the flat, only air and snow drag forces resist a
skier’s motion, requiring relatively modest propulsive forces to maintain skiing speed. On uphill terrain, gravity is an additional force against which
a skier is working. This requires greater propulsive forces to maintain uphill skiing speed. These
greater propulsive forces can be generated either
by increasing the resultant ski reaction forces, by
increasing the ski angle with respect to forward
direction (β in Eqn. 12.5 above) or by increasing the
ski edging angle on the snow surface (α). While no
force comparison of flat to uphill skiing is available,
on grades of 9 and 14% ski forces have been measured (Smith 1989). For these moderate and steep
uphills, average forces were similar while ski orientation angles changed with grade. Based on this
evidence, it is likely that skiers maintain similar
skating force magnitudes on different terrain but
generate greater propulsive force mainly through
adjustment of ski orientation and edging angles.
Ski orientation angle interacts with other kinematic characteristics of a skating stroke. As ski
angles increase away from the forward direction,
a skier’s lateral displacement during the stroke
increases and displacement in the forward direction
may decrease. The changing orientation angle of
a ski from flat to uphill terrain also results in a
modification to the effective slope up which the ski
is gliding. By angling the ski laterally, a skier can
increase the glide distance during a skating stroke
and the glide time before the ski speed decreases
substantially. Thus increased orientation angle of
the ski can accomplish two things—the propulsive
force component can be increased and uphill ski
glide can be enhanced. These come at the expense of
increased lateral motion, which may be constrained
by topology of the surroundings. As displacement
in the forward direction during a cycle decreases
with increased ski angle, a skier must increase the
skating stroke rate to maintain speed but this would
come at the expense of glide on each ski. At some
point, stroke rate limitations combined with race
course width limits restrict a skier’s ability to use
greater ski angles to increase propulsive force
without exceeding physiological optima.
Ski edging angle is a measure of a ski’s flatness
to the snow surface. It affects performance by in
factors affecting skiing performance
V1 skate
L. pole
L. ski
R. ski
R. pole
0
25
50
75
100
75
100
75
100
Per cent of full cycle
Open field skate
L. pole
L. ski
R. ski
R. pole
0
25
50
Per cent of full cycle
V2 skate
L. pole
L. ski
R. ski
R. pole
0
25
50
Per cent of full cycle
Fig. 12.20 Skating phase diagrams. Timing of the poling
and skating phases are shown for the V1, ‘open field’
(V2alt) and V2 skating techniques. (Data from Bilodeau
et al. 1992.)
part determining the propulsive force component
during a skating stroke and also by affecting ski
penetration into surface snow layers, which may
increase snow drag force while providing a firm
platform from which skating forces are generated.
Conventional wisdom from ski coaches suggests
that a ‘flat ski’ will glide faster than an edged ski. In
skating, glide directly affects cycle length. As faster
skiers tend to ski with greater cycle lengths it is a
265
common connection to relate ski edging to glide and
to performance. While it is reasonable to expect
snow drag forces to be greater on an edged ski than
on one that is flat (due to deeper penetration and
increased ploughing), this has not been demonstrated and the magnitude of the increased drag is
unknown. The typical description of fast skating
techniques like the V2 and the V2alt (open field)
includes a long glide phase on each ski prior to
pushing off with a vigorous knee extension. This
timing can be seen in the phase plots of Fig. 12.20
(Bilodeau et al. 1992). The implication of some
coaching suggestions is that a relatively static flat
ski position be maintained during the early parts
of each skating stroke where the ski is mainly
gliding.
However, this static flat ski emphasis is not typical of elite skiers (Smith & Heagy 1994). Figure 12.21
illustrates mean ski edging angles during fast skating on flat terrain during the men’s 50 km race at the
1992 Olympics. None of the 17 elite skiers analysed
in that study exhibited a ski edging phase where a
flat ski was statically maintained. Most skiers set
the ski down on the snow initially with it being
flat to the surface and all moved away from the
initial positioning immediately. Static posturing to
enhance ski glide has not been observed for elite
skiers and it is likely to be a disadvantageous skating technique. This observation must not be misunderstood to mean that ski edging and a flat ski are
unimportant characteristics for ski glide. Note in
Fig. 12.21 that despite smoothly increasing edging
angles on the strong side skate over the last 30% of
the cycle, the ski is only 10° from flat. This modest
amount of edging may have little effect on ski glide
while allowing a skier to dynamically stroke from
side to side. It is only later in each skating stroke
(Fig. 12.19), when ski reaction forces are largest, that
the skis are substantially edged. Several skiers of
this sample were observed to set the ski down on the
lateral edge (negative ski angle), rotate through
flat and onto the medial ski edge during the glide
phases on each side. This technique may be advantageous on flat, fast terrain as it may prolong the
time where the ski is within a few degrees of flat
while promoting a continuous dynamic movement
toward the next skating stroke.
266
locomotion
Ski-edging angle
Edging angle (degrees)
50
40
30
20
10
0
Weak-side skate
–10
0
20
40
Strong-side skate
60
Per cent of full cycle
Technique and equipment choices
In both classic and skating races, skiers employ a
variety of techniques in traversing the length of typical race courses. Technique choice in skiing is similar to gearing choices that cyclists make in riding
over variable terrain. On downhills, high gears
allow the continuation of pedalling without exceeding a cyclist’s cadence maximum. On flat terrain,
moderate gearing is used which allows riding at
optimal pedalling rates. On steep uphills, low gears
are used to minimize pedalling force demands and
to maintain cadence near optimal levels. Just as
cycling cadence is affected by gearing, in skiing, skicycle rates are affected by technique. And just as
cadence is affected by cycling speed and by terrain,
skiing speed and technique affect ski-cycle rate.
Similar factors probably influence a racer’s decisions about technique choices and about gearing.
While these have not been well researched, one can
conjecture that muscle strength and composition
in conjunction with cardiovascular characteristics
enter into the internal calculus of technique/gearing choice.
In classic skiing, typical techniques include
double-poling, kick double-pole, diagonal stride,
ski running, and herringbone (high to low ‘gearing’,
respectively). Skating technique can be similarly
ordered: V2, open field (V2alt), V1 and diagonal
skate. Cycle characteristics of the three primary
skating techniques and how these change with terrain have been most clearly researched (Boulay et al.
80
100
Fig. 12.21 Edging angle during open
field skating on flat terrain. Skating
phases are indicated by the heavy
lines; recovery phases (when the
ski is not in snow contact) by the
thin lines. Plots are mean ±SD
throughout a full cycle. Note that no
plateau region of near-zero angle
was observed. Skiers continuously
change edging angle throughout the
whole skating stroke. (From Smith &
Heagy 1994.)
1995). Figure 12.22 shows the typical decrease of skiing speed as slope increases. This response derives
almost completely from cycle length decreases
while cycle rates are almost constant for each technique across a range of slopes. With cycle rates of
about 0.6 Hz, the V2 technique is much like a high
gear where the slow cadence goes with a greater
displacement per cycle. In contrast, V1 is a higher
frequency (about 1 Hz), shorter cycle length technique rather like a lower gear. Open field skate is
somewhere in between these ‘gearings.’
The observations illustrated in Fig. 12.22 represent kinematic characteristics under near-maximal
skiing speed for each slope condition. Curiously,
skiing speeds on slight downhills or moderate
uphills were quite similar for the three techniques.
Only on more demanding uphills did the rate/
length differences in technique translate into
advantages for the ‘lower gear’ V1 technique. As
skiing speed increases beyond the 7 m · s–1 level
observed in the study by Boulay et al., it is likely that
V1 would become disadvantageous compared with
V2 and open field. While this comment is just conjecture, it is an easily measured relationship which
skiers can individually test.
Under racing conditions, very little time is spent
skiing at the maximal rates of the Boulay et al. (1995)
study. When skiing at submaximal speeds during
a race, performance is optimized in part by using
techniques which most economically match the
mechanical to the metabolic costs. While comprehensive physiological measurements have been
factors affecting skiing performance
55
6.0
50
VO2 (ml · kg–1 ·min–1)
Velocity (m ·s–1)
Mean oxygen uptake vs. technique at 3.9m ·s–1
V1
V2
Gunde
7.0
267
5.0
4.0
3.0
45
40
.
35
Cycle length (m · cycle–1)
2.0
30
12
VS
MS
KD
DI
Fig. 12.23 Submaximal Bo2 for double-poling (DP),
skating (VS), marathon skate (MS), kick double-pole (KD),
and diagonal stride (DI). (Data from Hoffman & Clifford
1990.)
10
8
6
4
3.9 m · s–1 on flat snow surface). Across several
studies, double-poling has consistently been more
‘economical’ than other techniques but has also
involved operating at greater percentages of technique-specific maximal oxygen uptake (Hoffman
et al. 1994) and at greater lactate levels (Mittelstadt
et al. 1995). This suggests that factors other than just
aerobic cost of a technique may affect performance.
2
Cycle rate (cycles · s–1)
DP
1.5
1.0
0.5
0.0
–1 0
6
9
14
Slope (per cent grade)
Fig. 12.22 Skating cycle characteristics as a function of
slope. The decreased speed observed as slope increases is
mainly due to cycle length changes while cycle rate stays
nearly constant. (Note: Gunde skate, open field and V2alt
are synonymous.) (From Boulay et al. 1995.)
completed for a variety of ski techniques (Hoffman
& Clifford 1990; Hoffman 1992; Hoffman et al.
1998), no direct comparisons of metabolic costs of
the primary skating techniques are available (see
Bilodeau et al. (1991) for estimates based on heart
rate response). In classic skiing, relative economy
of diagonal stride, kick double-pole and doublepoling have been measured on flat and uphill
terrain (Hoffman & Clifford 1992; Hoffman et al.
1994, 1998). Figure 12.23 illustrates the technique—
oxygen uptake response at constant velocity (about
Pole length
Double-poling relies strictly on the upper body to
generate propulsive force through the poles. It has
been extensively studied in recent years because of
the importance of poling to the skating techniques.
In classical diagonal stride, no systematic analysis of
pole vs. ski contributions to propulsion has been
published, but from Komi’s (1987) representative
graphs (Fig. 12.5) it appears that poling forces contribute modestly to diagonal stride performance.
In V1 skating uphill, poling forces have been found
to contribute about two-thirds of the propulsive
impulse driving a skier’s motion (Smith 1989). This
substantial component of skating makes optimizing
poling kinematics and kinetics an important aspect
of preparation. Skiers typically use poles for skating
which are 10 –15 cm longer than those used for
classical races. Little systematic investigation is
268
locomotion
available comparing the effects of pole length on
performance. In double-poling, Gibbons et al. (1992)
found no difference in physiological characteristics
in comparisons of long and short poles (about 89
and 83% of body height) for treadmill rollerskiing.
In contrast, Siletta (1987) simulated race conditions
on snow and compared performance with three
pole lengths (100, 105 and 110% of shoulder height).
The longest poles were overall advantageous for
seven of the nine skiers tested. All skiers were faster
skating uphill with the longest poles. The elbow
angle–pole angle relationship (Fig. 12.18) is likely to
be affected by the length of the pole. The nature of
this interaction is unknown currently. In the decade
since the study by Siletta, considerable fluctuation
of ‘recommended’ pole lengths has been distributed
by coaches and equipment suppliers. While skating
pole lengths even longer than the 110% (of shoulder
height) were popular for a few years, current conventional wisdom has moderated that recommendation somewhat. Without the results of a
systematic test of the effect of pole length on kinematic, kinetic and performance characteristics, we
can only speculate about how pole length influences
those characteristics.
Mechanical characteristics of poles change with
length. The most important of these characteristics
deal with mass and its distribution. While manufacturers of ski equipment take great pains to reduce
the mass of skis and poles, these items contribute a
small but not negligible proportion of the overall
energy cost of motion. Ski mass is lifted and accelerated with each stride or each skating stroke, requiring energy to accomplish the demands of each
technique. However, ski motion involves little rotation. In contrast, ski poles are rotated about an axis
near the handle during each cycle and pole moment
of inertia is a critical factor in pole design. Pole mass
(excluding basket and handle) may be less than
100 g in typical lengths and have a moment of
inertia as little as 0.06 kg m2. Adding a basket to
the shaft may increase overall mass by 15% or
more and increase moment of inertia by 32–49%
(Street & Tsui 1987)!
With longer ski poles, mass and especially
moment of inertia increase. These mechanical
characteristics directly affect the energy costs and
perhaps the kinematics of poling. The greater
moment of inertia of long poles will tend to increase
the time required to swing the pole forwards during
recovery, directly decreasing cycle rate. During
the poling phase, a longer pole may potentially
increase poling time, during which greater propulsive impulse may be generated but also decreasing
cycle rate as well. These competing advantages/
disadvantages change with pole length and suggest that some optimizing principle is involved.
Unfortunately, the details of that relationship are
not clearly understood at present.
Summary
Performance in cross-country skiing is affected by
ski and pole reaction forces, by snow and air drag
forces, and by gravity. Each of these resistive and
propulsive forces may be influenced by skier technique, body characteristics, equipment and environmental conditions. A general relationship of ski
racing which has been observed under many conditions of terrain and technique is that faster skiers
move with greater cycle lengths but similar cycle
rates to slower skiers. This chapter has addressed
some of the factors which elite skiers use to advantage and which allow them to ski faster than others.
Propulsive forces from skis and poles counter the
resisting forces of air and snow drag to maintain
constant velocity. Skiing optimally must involve
minimizing drag forces without degrading technique. Glide speed measurements clearly demonstrate that the fastest skiers start with the fastest
skis.
Ski reaction forces generate a major fraction of
propulsive force in diagonal stride. Timing of the
kick phase in diagonal technique generates an
optimal vertical force which produces a momentarily large static friction and very brief propulsive
impulse. In contrast, skating strokes are of considerably greater duration and depend on ski angles with
respect to the surface and to the forward direction to
create propulsive force. Edging of the ski probably
increases snow drag force. Optimal ski handling
involves sufficient edging of the ski to generate
some propulsive force without producing substantially larger drag force. However, because the
factors affecting skiing performance
propulsive component is a small fraction of the
resultant forces applied to a skating ski, poling
forces play a larger role in propelling a skater than is
true in diagonal stride. Measurements on uphill terrain suggest that poling is the major contributor to
skating propulsion.
Equipment characteristics can have a substantial
impact on skier technique and on performance. Ski
269
stiffness, pressure distribution and surface preparation affect how a ski interacts with a snow surface.
Pole characteristics can affect technique cycle rates,
propulsive components of force, and the energy
requirements to maintain skiing speeds. Optimal
ski performance involves all these factors to minimize the mechanical costs of skiing at maximally
sustainable metabolic rates.
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PART 3
JUMPING AND AERIAL MOVEMENT
Chapter 13
Aerial Movement
M.R. YEADON
Introduction
Most sports movements have an aerial phase. In
sprinting the runner spends less than half of the
time in contact with the ground (Hopper 1973),
while in the triple jump the aerial phases are much
longer than the contact phases (Hay & Miller 1985).
Typically tennis players are off the ground when the
ball is played (Elliott 1989) and basketball players
release the ball while airborne (Hay 1993). The same
is true for the release in the discus and shot events
(Hay 1993). In jumping activities it is the aerial
phase that is evaluated to give a score for the performance. In the long jump and high jump events the
horizontal and vertical displacements during the
aerial phase are used as measures of performance,
while in trampolining and diving rotation and aesthetics are also included in the evaluation.
In an aerial phase of a sports movement the
athlete is freely falling under gravity. In freefall the
balance mechanisms of the inner ear do not oper-
ate normally since they too are in freefall (Graybiel
1970). The otolith and semicircular canals can no
longer provide information on the orientation of
the head relative to the vertical direction. They do,
however, give information on linear and angular
accelerations (Wendt 1951) which can be used by
athletes to help control aerial movements (Yeadon
& Mikulcik 1996).
Motion of the mass centre
In the aerial phases of most sporting movements, air
resistance has little effect and the path of the mass
centre follows a parabola that is determined by the
position and velocity of the mass centre at takeoff. In
the competition performance shown in Fig. 13.1 the
height of the mass centre at takeoff is 1.31 m while
the horizontal and vertical velocities are 4.7 m · s–1
and 4.5 m · s–1. During the aerial phase the horizontal velocity of the mass centre remains constant
since there are no horizontal forces acting (if air
Fig. 13.1 The flight phase of a highjump performance showing the
parabolic path of the mass centre.
273
274
jumping and aerial movement
resistance is neglected) while the vertical motion has
a constant downwards acceleration of 9.81 m · s–2
due to the weight of the body. The vertical takeoff velocity of 4.5 m · s–1 determines that the mass
centre rises to a peak height of 2.34 m in a time of
0.46 s. The horizontal takeoff velocity of 4.7 m · s–1
determines that the mass centre covers a horizontal
distance of 2.16 m during this time.
In the case of ski jumping, however, the takeoff
parameters do not completely determine the path of
the mass centre during flight since air resistance
produces drag and lift forces which can be used by
the skilled jumper to maximize the distance of the
jump (Denoth et al. 1987; Hubbard et al. 1989).
Fig. 13.2 A double backward somersault from a floor
exercise showing the increased speed of somersault
rotation when the body is tucked.
Rotation during flight
In running jumps, the takeoff phase typically produces rotation even where this is disadvantageous
to the performance. In long-jumping undesirable
forward angular momentum is produced during
the takeoff and a hitch-kick, involving arm and leg
rotations, is often used to minimize the forward
rotation in the aerial phase (Hay 1975; Herzog 1986).
In high-jumping, both twist and somersault rotations are produced during takeoff and these are
used to advantage in clearing the bar (Hopper 1963;
Dapena 1980, 1995). In gymnastics skills, the somersault is initiated during the takeoff phase, while
twist may be initiated either during the takeoff
or during the aerial phase (van Gheluwe 1981).
Although the movement of the mass centre is predetermined at takeoff (so long as air resistance can be
neglected) the athlete has considerable control over
rotational motion during the aerial phase.
At takeoff a gymnast has a certain quantity of
angular momentum about the mass centre and this
remains constant during the aerial phase since the
only force acting is the weight of the gymnast and
this force acts through the mass centre. For the simple case in which the body rotates about a single axis
the angular momentum is the product of moment of
inertia and angular velocity. A ballet dancer or a
figure skater takes off for a twisting jump with arms
wide and subsequently brings the arms close to the
body. The effect of this is to reduce the moment of
inertia about the twist axis and to increase the speed
of rotation. In the double somersault shown in
Fig. 13.2 taken from a floor exercise at the 1996
Olympic Games, the gymnast is initially in an extended configuration and is somersaulting relatively
slowly, whereas subsequently the gymnast adopts a
tucked position which has a smaller moment of
inertia so that the somersault rate increases. By
extending again at an appropriate time the gymnast
can land the skill on the feet and maintain balance.
For twisting somersaults in which rotations take
place about more than one body axis, the situation
is more complex but the same principle of angular momentum conservation governs the motion
(Yeadon 1993a).
Somersaulting
While a gymnast has considerable control over the
rotation in the aerial phase the angular momentum
for a specific skill is often quite tightly constrained
by the requirements for the good performance.
Figure 13.3 depicts a good performance of a double
somersault dismount from the high bar in a straight
or extended position. Since the gymnast must remain extended throughout the aerial phase he has
only a limited ability to adjust his moment of inertia,
primarily by changing arm position. As a consequence the angular momentum generated prior to
release must lie within fairly tight limits in order for
a good performance to be possible. The angular
aerial movement
Fig. 13. 3 A double somersault dismount from the high
bar with a straight body.
momenta in four double somersault dismounts
from the high bar in Olympic competition varied by
as much as 16% although only one of the dismounts
could be considered to demonstrate a good straight
position during flight (Kerwin et al. 1990).
For body positions other than straight there is
more freedom for the gymnast to adjust the somersault rate. In the tucked triple somersault dismount
from high bar shown in Fig. 13.4 there is sufficient
angular momentum to allow the movement to be
completed successfully. If there were slightly less
angular momentum than this, the gymnast could
compensate by adopting a tighter tucked position.
There could, however, be considerably more angular momentum without this being detrimental to a
good performance. With more angular momentum
the gymnast could delay the movement into the
tucked position and could extend earlier prior to
landing. In fact the angular momentum of the
straight double somersault shown in Fig. 13.3 is 18%
greater than the angular momentum of the tucked
triple somersault shown in Fig. 13.4. This indicates
that a gymnast who can do a straight double somer-
Fig. 13.5 During a wobbling
somersault the twist oscillates left
then right.
275
Fig. 13.4 A triple somersault dismount from the high bar
with the body tucked.
sault dismount from high bar should be able to
generate ample angular momentum for a tucked
triple somersault dismount. Some gymnasts have
employed a split tuck technique in which the knees
are pulled wide to reduce the moment of inertia
about the somersault axis, but this technique is a
break in form and only marginally increases the
somersault rotation (Kerwin et al. 1990).
Twisting
To understand the mechanics of a multilink system
performing somersaults with twist, it is helpful to
look at the rotational motion of a rigid body. There
are only two general types of motion that a rigid
body can exhibit (Yeadon 1993a). The first of these is
the wobbling somersault in which the body somersaults about a horizontal axis but also has an oscillating motion in which it twists one way and then
the other (Fig. 13.5). During this motion the body
also tilts first one way and then the other so that the
head is to one side of the feet and then later to the
other (see the first and last images in Fig. 13.5).
276
jumping and aerial movement
Fig. 13.6 During a twisting
somersault the twist continues in one
direction.
The second type of motion is the twisting somersault in which the twist is always in the same direction (Fig. 13.6). During this motion the body is
always tilted in the same direction away from the
somersault plane (the plane normal to the angular
momentum vector). This tilt varies with the twist
and is smallest for an even number of quarter twists
(images 1, 6 and 11 of Fig. 13.6) and greatest for an
odd number of quarter twists (images 3 and 9 of Fig.
13.6). This variation in the tilt angle is known as
nutation from the theory of spinning tops (Synge &
Griffith 1959) and is important for the understanding of how aerial twist is produced (Yeadon 1993c).
Since there are two quite different types of rigid
body motion it might be possible that a multilink
system such as the human body could change its
motion from one type to the other merely by changing body configuration.
Contact twist
Angular momentum is built up while the body is in
contact with the diving board or gymnastics apparatus so that it is somersaulting at takeoff. Twist may
be initiated in a similar way by turning the arms and
trunk in the direction of the twist while the feet are
in contact with the takeoff surface. If the body is
extended at takeoff this will produce a twisting
somersault in which the body is tilted away from
the vertical after half a somersault (Eaves 1969;
Biesterfeldt 1974). Because this tilt disappears of its
own accord after a complete somersault, it does not
pose a problem in tumbling skills in which the gymnast takes off and lands on the feet. In twisting
dives, however, there is a potential problem since
entry is made into the water after one and a half
somersaults. In the computer simulation shown in
Fig. 13.7 the body maintains left–right symmetry
throughout (upper sequence in Fig. 13.7) and overcomes this potential problem by adopting a piked
position as the required number of twists nears
completion. This causes the motion to change from
a twisting somersault to a wobbling somersault.
While the body is in the wobbling mode of motion
the tilt angle is allowed to oscillate so that when the
body extends it is almost vertical. This technique
has its limitations since for large amounts of twist
the wobble in the piked position becomes excessive
and the twist is much harder to control (Yeadon
1993b).
Fig. 13.7 A computer simulation of a
backward 11/2 somersault dive with 11/2
twists in which the twist is produced
during the takeoff.
aerial movement
Aerial twist
The way in which a cat rights itself by producing
a half twist in mid-air after being dropped in an
inverted position has been studied for more than
a century (Marey 1894; McDonald 1960). Some
coaches have thought that this is the main mechanism that divers use to produce twist (Rackham
1960; Eaves 1969). The twist is produced by using a
hula-hoop circling movement of the hips during the
aerial phase. If the initial angular momentum is zero
it must remain so during flight and so the angular
momentum associated with the hip circling produces a twisting of the whole body in the opposite
direction (Kane & Scher 1969). A simulation of this
movement is shown in Fig. 13.8 in which the hips
circle to the right producing a twist to the left. The
body moves from a forward flexed position through
a side arch over the right hip, into a back arch,
Fig. 13.8 Computer simulation of an aerial half twist
using the ‘hula’ or ‘cat’ technique.
Fig. 13.9 Aerial twist in a somersault
resulting from tilt produced by
asymmetrical arm movement.
277
through a side arch over the left hip and ends in a
forward flexed position again, having completed a
half twist. A skilled trampolinist can produce a full
twist using two cycles of such a movement while
airborne.
It is evident that gymnasts, trampolinists and
divers do not use this hula technique to produce
multiple twists during the aerial phase of a somersault since the body typically remains straight during the twist. If somersault is present then any
technique that tilts the body away from the somersault plane will result in twist in order to maintain
constant angular momentum (Frolich 1980). The
most obvious way of producing tilt during freefall is
to raise one arm laterally while lowering the other.
In a plain jump there is no angular momentum
and this arm movement will produce a tilting of
the whole body in order to maintain zero angular
momentum (upper sequence of Fig. 13.9). If the
same arm movements are made during a plain somersault, a similar amount of tilt (8°) results and the
body automatically twists in order to maintain constant angular momentum (Yeadon 1990).
Any movement in which left–right symmetry is
not maintained is likely to produce some twist. In
the simulation shown in Fig. 13.10 the body makes a
partial hula movement while extending from a
piked to a straight position. In a plain jump this hula
movement with wide arms produces tilt while the
body is in a side arch configuration due to a reorientation of the principal axes of inertia (Yeadon &
Atha 1985). Once the body extends, however, the
278
jumping and aerial movement
Fig. 13.10 Aerial twist in a
somersault resulting from tilt
produced by asymmetrical hip
movement.
final tilt is only 3° (upper sequence of Fig. 13.10). If
the same movements are made during a somersault
the situation is somewhat different. Once the body
is in a side arch position with wide arms there is
considerable tilt (10°) of the principal axis corresponding to minimum moment of inertia and so the
body starts to twist in order to maintain constant
angular momentum. As the twist increases up to a
quarter twist, the tilt angle also increases due to the
nutation effect. When the body extends to a straight
position the tilt angle is not reduced in the same
way as for a plain jump with a hula movement since
this extension is made at around the quarter twist
position and any reorientation therefore changes
the somersault rather than the tilt. As a consequence
this technique produces considerable tilt (11°) in a
somersault and is a viable method of producing
aerial twist.
It is fortuitous that the hula movement that produces a twist to the left in a jump also produces tilt
which will result in a twist to the left in a forward
somersault. During the takeoff for a forward somersault from the floor or trampoline or diving board
the body flexes at the hips so that initially it is in a
piked position which is suitable for this technique.
For a backward somersault the body is initially
arched and use of a partial hula movement while
extending again produces tilt which results in twist
in the same direction as the hula twist. If the body is
rotating backwards in a piked position, however, the
tilt produced by a hula movement results in twist in
the opposite direction to the hula twist. This conflict
greatly reduces the effectiveness of the technique
(Yeadon 1993c) and it is preferable to use asymmetrical arm movement to produce aerial twist from a
piked configuration when rotating backwards.
The tilt produced by an asymmetrical arm movement will be greater when the arms move through a
large angle. In order to achieve this in a computer
simulation, the left arm is first lowered to the side of
the body together with some adduction and abduction so that it passes in front of the body (upper
sequence of Fig. 13.11). This minimizes the negative
tilt produced by the initial arm movement and
places the arms in an asymmetrical position from
which each arm may be rotated through half a revolution. This produces twice the tilt (16°) of the arm
movement shown in Fig. 13.9 since the arms move
through twice the angle. When the same arm
movements are made during a somersault a similar
amount of tilt results and a rapid twist ensues
(lower sequence of Fig. 13.11). As the twist nears
three revolutions the body flexes at the hips and the
arms are spread wide. This removes the tilt so that a
one and a half somersault dive with three twists can
be completed. It is important that the left arm initially sweeps across the body as it is lowered to the
side as otherwise the body becomes tilted in the
opposite direction and twists to the right while
the arm is being lowered. In this case the double
aerial movement
279
Fig. 13.11 Simulation of a forward 11/2
somersault dive with three twists
using asymmetrical movements of
the arms.
arm movement occurs around the quarter twist
position and produces little change in the tilt angle
since the reorientation of the body manifests itself
mainly as a change in somersault rotation.
The asymmetrical hip technique shown in Fig.
13.10 may be used to produce one and a half twists
in a single or double somersault. In Yeadon (1997a)
a progression based on computer simulations is
described for learning a double somersault with
one and a half twists in the second somersault
(Fig. 13.12). In the first somersault the body is flexed
into a piked position and then moves through a side
arch position with wide arms while extending. The
arms are then adducted to accelerate the twist and
as the one and a half twists are completed first the
right arm and then the left arm is abducted to help
remove the tilt. The body also moves through a side
arch position while flexing in order to use the asymmetrical hip technique to help remove the tilt. The
asymmetrical hip technique is capable of producing
tilt when the somersault is forwards and of removing tilt when the somersault is backwards. It is not
effective in removing the tilt in a dive such as in
Fig. 13.12 A double somersault with
11/2 twists in the second somersault
produced using asymmetrical hip
movement.
Fig. 13.11 where the final somersault direction is
forwards.
Stopping the twist
In the simulation shown in Fig. 13.11 tilt was
removed using a reversal of the initial asymmetrical
arm movement that was used to produce the tilt.
This technique may be used in dives with an even
number of half twists. For an odd number of half
twists a reversal of the initial arm movement would
increase the tilt and speed up the twist. In such a
case it is necessary to reverse the arm positions
during the twist without affecting the tilt so that
they are in a suitable position for removing the tilt
prior to entry. In backward and reverse twisting
dives there are typically 11/2 , 2 1/2 or 31/2 twists, and this
technique is often used. The lower sequence of
Fig. 13.13 is taken from a performance of a backward 11/2 somersault dive with 11/2 twists. The upper
sequence shows the body configurations used in the
dive. After takeoff the left arm is lowered and the
right arm is held high producing tilt that results in a
280
jumping and aerial movement
Fig. 13.13 Stopping the twist by
removing the tilt in a backward 11/2
with 11/2 twists using asymmetrical
arms.
twist to the left. During the twist the arm positions
are reversed while keeping the arms close to the
body so as not to slow the twist. As the 11/2 twists
near completion the diver first pikes and then
lowers his left arm while raising his right arm so as
to remove the tilt. By first flexing at the hips the
moment of inertia about the frontal axis is reduced
so that more tilt can be removed by the asymmetrical arm movement.
Contributions of twisting techniques
to tilt and twist
The simulation model of Yeadon et al. (1990a) has
been used to determine the contributions of the various twisting techniques to the production of tilt
and hence twist in actual performances by using
modifications of the body configurations used by
the athlete. To determine the contribution of asymmetrical arm movement, for example, a modified
simulation can be carried out in which the right arm
mirrors the original left arm movement so that the
arms move symmetrically. The difference in the tilt
angles produced in this simulation and the original
simulation based on the actual arm movement gives
a measure of the contribution to the tilt angle from
asymmetrical arm movement (Yeadon 1993d). Other
contributions can be determined in a similar manner.
Figure 13.14 depicts a performance of a double
somersault from trampoline with a full twist in the
second somersault. In such a movement, where
almost a complete somersault occurs prior to the initiation of twist, it is to be expected that little contact
twist is used and that aerial techniques are responsible for the production of twist. Prior to twisting the
body is piked and since it is rotating backwards
asymmetrical hip movement is unable to produce
much tilt since the directions of hula twist and tilt
twist are in conflict. As a consequence it might be
expected that the twist is produced by asymmetrical
arm movement in the aerial phase, and a simulation
analysis yields just this result (Yeadon 1993d).
Such simulation analyses have shown that the
greatest contributions are made by asymmetrical
arm and hip techniques in the aerial phase in springboard diving (Yeadon 1993e), in single somersault
Fig. 13.14 Performance of a
double backward somersault from
trampoline with one twist in the
second somersault.
aerial movement
281
Fig. 13.15 Simulation of an unstable
double backward somersault leading
to a quarter twist.
dismounts with one twist from high bar (Yeadon
et al. 1990b) and in double somersault dismounts
with one twist from the rings (Yeadon 1994). There
is some evidence, however, that major contributions
are made by contact techniques in multiple somersaults with twist when there is substantial twist in
the first somersault in, for example, high bar dismounts (Yeadon 1997b) and freestyle aerial skiing
(Yeadon 1989).
Control of aerial movement
If a rigid body is somersaulting about its intermediate principal moment of inertia the motion is
unstable in the sense that twist will build up exponentially until the body completes a half twist
(Marion 1965; Hinrichs 1978). In practice this will
pose a potential problem for somersaults about a
lateral axis when the body is held straight. Figure
13.15 depicts a hypothetical simulation of a double
somersault in which slight arm asymmetries lead
to a quarter twist towards the end of the movement. Nigg (1974) suggested that the arms could be
extended laterally during a straight somersault in
order to minimize the effect of this instability.
Yeadon and Mikulcik (1996) showed that this strategy will not decrease the build-up of twist. An alternative strategy of asymmetrical arm adduction and
Fig. 13.16 A performance of a double
straight somersault in which
corrective arm asymmetry is
apparent late in the movement.
Fig. 13.17 Simulation of a double
backward somersault with one twist
in the second somersault arising from
slight arm asymmetry in the first
somersault.
abduction based upon the twist angular velocity
and acceleration is capable of preventing the buildup of twist providing that the time delay in the feedback loop is less than a quarter of a somersault.
There is evidence that the inner ear organs normally
used for balance provide the required feedback data
on twist velocity and acceleration rather than the
visual system (Yeadon & Mikulcik 1996). The main
function of the eyes may be to obtain angular information on body orientation in space in order to
make in-flight adjustments for correct landing orientation (Rezette & Amblard 1985).
In actual performances of straight double somersaults such asymmetrical arm movements are not
readily apparent to an observer or to the performer
making the corrective adjustments. This is probably
because the corrective movements made are small
and the build-up of twist is small. Occasionally,
however, the build-up of twist may be corrected
somewhat late and a larger arm asymmetry will be
required. An example of such a case is shown in
Fig. 13.16 which depicts an actual performance of a
double straight somersault on trampoline in which
considerable arm asymmetry is evident after 11/2
somersaults.
The build-up of twist can be used to good effect to produce an aerial twist using only a small
asymmetry in the arm positions. Figure 13.17 depicts
282
jumping and aerial movement
a theoretical simulation of a double somersault
with one twist in the last 11/4 somersaults. During
the first three-quarters of a somersault the arms
are spread wide but with a small (5°) asymmetry.
This leads to a slow build-up of tilt and twist during
the first somersault. The twist is accelerated by
adducting both arms towards the end of the first
somersault. As one revolution of twist nears completion, first the right arm is adducted and then the
left arm in order to remove the tilt and stop the
twist. Since this asymmetrical arm movement for
stopping the twist comprises exactly the same technique as that for preventing the build-up of twist
in a straight somersault it is likely that learning this
type of control in a twisting somersault is carried
over into the control of non-twisting somersaults
or vice versa.
Summary
Most sports movements contain an aerial phase
during which the body loses contact with the
ground or apparatus. While the path of the mass
centre during flight is determined by its location
and velocity at takeoff, the amount and type of rotation of the body is largely under the control of the
athlete. Somersault rotation is a consequence of
the angular momentum generated during takeoff.
Twist rotations may be initiated during takeoff or
during the aerial phase by means of asymmetrical
arm or hip movements. Asymmetrical arm movements may be used to stop the twist in a twisting
somersault or to prevent the build-up of twist in a
non-twisting somersault. The control of the twist in
this way is possible using feedback via the inner ear
balance mechanisms, provided that the somersault
rate is not too high.
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Chapter 14
The High Jump
J. DAPENA
Introduction
This chapter describes the mechanics of the
Fosbury-flop style of high jumping, and explains a
rationale followed for the evaluation of the techniques used by individual elite high jumpers.
Since 1982, our laboratory has studied the techniques of the best high jumpers in the USA. This work
is part of the Scientific Support Services programme
sponsored by USATF (USA Track and Field, the
governing body for track and field athletics in the
USA) at several biomechanics laboratories. The goal
of the programme is to give the best US athletes
biomechanical information to help improve their
performance through changes in technique.
Personnel from our laboratory generally film the
top American high jumpers every year at the final of
the USATF Championships or at some other major
competition. The films are subsequently analysed
using three-dimensional biomechanical research
Table 14.1 General information on the analysed jumpers, and meet results.
Standing
height (m)
Mass
(kg)
Personal best
mark* (m)
Best height cleared
at the meet† (m)
USSR
USA
Australia
USSR
Poland
Sweden
Cuba
USA
Czechoslovakia
2.02
1.84
1.97
1.91
1.91
2.00
1.94
1.95
1.91
82
68
75
72
73
82
82
82
85
2.38
2.40
2.34
2.41
2.37
2.42
2.44
2.34
2.36
2.38 (W87)
2.34 (O92)
2.34 (O92)
2.38 (W87)
2.34 (O92)
2.34 (O92)
2.34 (O92)
2.34 (T84)
2.34 (W87)
USA
Romania
East Germany
Bulgaria
Germany
Bulgaria
Cuba
USA
1.88
1.84
1.78
1.69
1.82
1.80
1.80
1.76
64
65
58
55
63
60
60
58
1.98
2.00
2.02
2.00
2.07
2.08
1.98
2.00
1.96 (U97)
2.00 (O92)
2.02 (W87)
2.00 (W87)
2.02 (O92)
2.05 (W87)
1.97 (O92)
1.96 (U87)
Athlete
Country
Men
Gennadiy Avdeyenko
Hollis Conway
Tim Forsyth
Igor Paklin
Artur Partyka
Patrik Sjöberg
Javier Sotomayor
Dwight Stones
Jan Zvara
Women
Amy Acuff
Galina Astafei
Susanne Beyer-Helm
Emilia Dragieva
Heike Henkel
Stefka Kostadinova
Ioamnet Quintero
Coleen Sommer
* By the end of the meet in which the jumper was analysed.
† T84 = 1984 US Olympic Trials; W87 = 1987 World Indoor Championships; U87 = 1987 USATF Championships;
O92 = 1992 Olympic Games; U97 = 1997 USATF Championships.
284
the high jump
methods. Reports and videotapes containing mechanical data, computer graphics and interpretations
are then prepared, and sent to the coaches and
athletes. The reports and videotapes evaluate the
advantages and disadvantages of the present techniques of the athletes, and suggest how to correct some
of the technique problems. The rationale used for the
technique evaluations stems from a comprehensive
interpretation of the Fosbury-flop style of high jumping based on the research of Dyatchkov (1968) and
Ozolin (1973), on basic research carried out by the
author and collaborators (Dapena 1980a,b, 1987,
1995a,b, 1997; Dapena & Chung 1988; Dapena et al.
1990, 1997c), and on the experience accumulated
through the analysis of US and other high jumpers at
our laboratory since 1982 in the course of service work
sponsored by USATF, the USOC (United States Olympic Committee), and the IOC (International Olympic
Committee) (e.g. Dapena et al. 1993a,b, 1997a,b).
The main purpose of this chapter is to describe
this interpretation of the Fosbury-flop style of high
jumping, and to explain the rationale followed in
the reports for the evaluation of technique. The discussions are illustrated with data from the highest
jumps by men and women in our database. Table
14.1 shows general information on these athletes,
and their results in the analysed competitions. They
all used the Fosbury-flop style.
phase, the most important phase of the jump. The
actions of the athlete during the bar clearance are
less important: Most of the problems found in the
bar clearance actually originate in the run-up or
takeoff phases.
General characteristics of the run-up
The typical length of the run-up for experienced
high jumpers is about 10 steps. In most athletes who
Takeoff point
Radius of
the curve
Start of
the curve
Phases of a high jump
A high jump can be divided into three parts: the runup phase, the takeoff phase and the flight or bar
clearance phase. The purpose of the run-up is to set
the appropriate conditions for the beginning of the
takeoff phase. During the takeoff phase, the athlete
exerts forces that determine the maximum height
that the centre of mass (COM) will reach after leaving the ground and the angular momentum (or
‘rotary momentum’) that the body will have during
the bar clearance. The only voluntary movements
that can be made after leaving the ground are internal compensatory movements (e.g. one part of the
body can be lifted by lowering another part; one
part of the body can be made to rotate faster by making another part slow down its rotation).
The run-up serves as a preparation for the takeoff
285
Centre of the curve
Start of the run-up
Fig. 14.1 Sketch of the run-up.
286
jumping and aerial movement
use the Fosbury-flop technique, the first part of the
run-up usually follows a straight line perpendicular
to the plane of the standards, and the last four or five
steps follow a curve (Fig. 14.1). One of the main purposes of the curve is to make the jumper lean away
from the bar at the start of the takeoff phase. The
faster the run-up or the tighter the curve, the greater
the lean towards the centre of the curve.
last two footprints; p2 and p1 are the angles between
the bar and the path of the COM in the airborne
phases of the last two steps; p0 is the angle between the bar and the path of the COM during the
airborne phase that follows the takeoff. The angles
are smaller in athletes who move more parallel to
the bar. The values of these angles are shown in
Table 14.2.
Approach angles
Progression of the run-up
Figure 14.2 shows an overhead view of the footprints and of the COM path during the last two
steps of the run-up, the takeoff phase and the airborne phase. Notice that the COM path is initially to
the left of the footprints. This is because the athlete is
leaning towards the left during the curve. The path
then converges with the footprints, and the COM is
almost directly over the takeoff foot at the end of the
takeoff.
Figure 14.2 also shows angles t1, p2, p1 and p0: t1 is
the angle between the bar and the line joining the
To start the run-up, the athlete can either walk a few
steps and then start running, or make a standing
start. In the early part of the run-up, the athlete
should follow a gradual progression in which each
step is longer and faster than the previous one. After
a few steps, the high jumper will be running rather
fast, with long, relaxed steps similar to those of a
400-metre or 800-metre runner. In the last two or
three steps of the run-up the athlete should gradually lower the hips. This has to be done without a
significant loss of running speed.
COM path
TOD
p0
COM position at the end
of the takeoff phase
p1
SL1
t1
p2
COM path
Fig. 14.2 Footprints and centre of
mass (COM) path.
the high jump
287
Table 14.2 Direction of the footprints of the last step (t1), direction of the path of the centre of mass (COM) in the last two
steps (p2 and p1) and after takeoff (p0), direction of the longitudinal axis of the foot with respect to the bar (e1), with respect
to the final direction of the run-up (e2) and with respect to the horizontal force made on the ground during the takeoff
phase (e3), length of the last step (SL1, expressed in metres and also as a percentage of the standing height of the athlete),
and takeoff distance (TOD).
SL1
Athlete
t1
(°)
p2
(°)
p1
(°)
p0
(°)
e1
(°)
e2
(°)
e3
(°)
(m)
(%)
TOD
(m)
Men
Avdeyenko
Conway
Forsyth
Paklin
Partyka
Sjöberg
Sotomayor
Stones
Zvara
33
15
26
32
28
26
31
32
33
54
47
46
50
51
48
–
55
55
44
30
39
40
41
37
41
44
43
39
34
38
33
33
29
31
38
44
23
−9
17
4
16
11
11
−5
23
21
39
21
36
25
26
30
50
20
25
36
22
43
35
35
40
56
20
2.27
2.11
2.18
2.16
1.83
2.10
2.31
2.00
2.11
112
115
111
113
96
105
119
102
111
0.96
0.94
0.91
0.86
1.01
0.77
0.84
0.99
0.67
Women
Acuff
Astafei
Beyer-Helm
Dragieva
Henkel
Kostadinova
Quintero
Sommer
23
32
29
33
30
34
30
23
50
–
50
47
55
51
51
44
36
39
42
41
41
43
42
36
33
34
40
40
38
37
34
33
18
21
24
31
42
26
27
30
18
18
18
10
−1
16
14
6
22
24
20
11
4
24
24
11
1.69
2.00
1.80
1.85
1.91
2.06
1.91
1.72
90
109
101
109
105
114
106
98
0.53
0.88
1.04
0.82
0.94
0.98
0.75
0.90
Note: Some of the values in this table may not fit perfectly with each other, because of rounding off.
Horizontal velocity and height of
the COM at the end of the run-up
The takeoff phase is defined as the period of time
between the instant when the takeoff foot first
touches the ground (touchdown) and the instant
when it loses contact with the ground (takeoff).
During the takeoff phase, the takeoff leg pushes
down on the ground. In reaction, the ground pushes
up on the body through the takeoff leg with an equal
and opposite force. The upward force exerted by the
ground on the athlete changes the vertical velocity
of the COM from a value that is initially close to zero
to a large upward vertical velocity. The vertical
velocity of the athlete at the end of the takeoff phase
determines how high the COM will go after the
athlete leaves the ground, and is therefore of great
importance for the result of the jump.
To maximize the vertical velocity at the end of the
takeoff phase, the product of the vertical force
exerted by the athlete on the ground and the time
during which this force is exerted should be as large
as possible. This can be achieved by making a large
vertical force while the COM travels through a long
vertical range of motion during the takeoff phase.
A fast approach run can help the athlete to exert a
larger vertical force on the ground. This can occur in
the following way. When the takeoff leg is planted
ahead of the body at the end of the run-up, the knee
extensor muscles resist the flexion of the leg, but the
leg is still forced to flex because of the forward
momentum of the jumper. In this process the extensor muscles of the knee of the takeoff leg are
stretched. It is believed that this stretching stimulates the muscles, which in turn allows the foot of
the takeoff leg to exert a larger force on the ground.
288
jumping and aerial movement
Table 14.3 Height of the centre of mass (COM) at the start of the takeoff phase (hTD, expressed in metres and also as a
percentage of the standing height of the athlete), horizontal velocity in the last two steps of the run-up (vH2 and vH1),
horizontal velocity after takeoff (vHTO), change in horizontal velocity during the takeoff phase (∆vH), vertical velocity at
the start of the takeoff phase (vZTD), and vertical velocity at the end of the takeoff phase (vZTO).
hTD
Athlete
(m)
(%)
vH2
(m · s−1)
vH1
(m · s−1)
vHTO
(m · s−1)
∆vH
(m · s−1)
vZTD
(m · s−1)
vZTO
(m · s−1)
Men
Avdeyenko
Conway
Forsyth
Paklin
Partyka
Sjöberg
Sotomayor
Stones
Zvara
0.92
0.78
0.95
0.85
0.93
0.98
0.89
0.92
0.89
45.5
42.5
48.5
44.5
48.5
49.0
46.0
47.0
46.5
8.1
7.4
7.2
8.1
7.6
7.2
–
7.0
6.9
7.9
7.4
7.3
7.7
7.4
7.5
8.0
7.1
6.6
3.7
3.4
3.8
3.9
4.1
4.0
4.0
3.5
2.6
−4.2
−4.0
−3.4
−3.9
−3.3
−3.5
−4.0
−3.5
−4.0
−0.3
−0.6
−0.6
−0.5
−0.6
−0.6
−0.7
−0.4
−0.6
4.50
4.65
4.55
4.55
4.50
4.25
4.60
4.40
4.65
Women
Acuff
Astafei
Beyer-Helm
Dragieva
Henkel
Kostadinova
Quintero
Sommer
0.92
0.88
0.86
0.81
0.89
0.90
0.84
0.87
49.0
48.0
48.0
47.5
49.0
50.0
46.5
49.5
6.3
–
6.9
6.9
7.4
7.5
7.3
6.9
6.3
7.2
7.2
7.2
7.2
7.3
6.7
7.1
3.5
4.1
3.8
3.5
4.3
4.2
3.8
4.3
−2.8
−3.1
−3.4
−3.7
−2.9
−3.1
−2.9
−2.8
−0.2
−0.7
−0.5
−0.8
−0.5
−0.5
−0.8
−0.6
3.80
3.95
4.00
4.10
3.90
4.00
3.90
3.85
Note: Some of the values in this table may not fit perfectly with each other, because of rounding off.
In this way, a fast run-up helps to increase the
vertical force exerted during the takeoff phase. (For
a more extended discussion of the mechanisms that
may be involved in the high jump takeoff, see
Dapena & Chung 1988.) Table 14.3 shows the values
of vH2, the horizontal velocity of the athlete in the
next-to-last step of the run-up, and of vH1, the horizontal velocity of the athlete in the last step of the
run-up, just before the takeoff foot is planted on the
ground. The value of vH1 is the important one.
To maximize the vertical range of motion through
which force is exerted on the body, the centre of
mass needs to be in a low position at the start of the
takeoff phase and in a high position at the end of it.
The COM of most high jumpers is reasonably high
by the end of the takeoff phase, but it is difficult to
have the COM in a low position at the start of the
takeoff phase. This is because in such a case the body
has to be supported by a deeply flexed non-takeoff
leg during the next-to-last step of the run-up, which
requires a very strong non-takeoff leg; it is also
difficult to learn the appropriate neuromuscular
patterns that will permit the athlete to pass over the
deeply flexed non-takeoff leg without losing speed.
Table 14.3 shows the value of hTD, the height of the
COM at the instant that the takeoff foot is planted on
the ground to start the takeoff phase. It is expressed
in metres, but also as a percentage of the standing
height of each athlete. The percentage values are
more meaningful for comparing athletes.
It is possible to achieve an approach run that is
fast and low in the last steps. However, it requires
considerable effort and training. If an athlete has
learned how to run fast and low, a new problem
could occur: The athlete could actually be too fast
and too low. If the takeoff leg is not strong enough, it
will be forced to flex excessively during the takeoff
phase, and then it may not be able to make a forceful
the high jump
50
289
KOS
SOM
HEN
ACU
BEY
AST
48
PAR
SJO
FOR
hTD (%)
DRA
ZVA
QUI
STO
SOT
46
AVD
PAK
44
Fig. 14.3 Horizontal velocity at the
end of the run-up (vH1) and height
(hTD) of the centre of mass (COM)
at the end of the run-up.
CON
42
6.2
extension in the final part of the takeoff phase. In
other words, the takeoff leg may suffer partial or
complete collapse (buckling) under the stress, and
the result will be an aborted jump. Therefore, it is
important for a high jumper to find the optimum
combination of run-up speed and COM height. We
will now see how this can be done.
Figure 14.3 shows a plot of hTD vs. vH1. Each
point represents one jump by one athlete. (A different symbol has been assigned to each athlete in
Fig. 14.3; the same symbol will be used in subsequent graphs.) This kind of graph permits one to
visualize simultaneously how fast and how high an
athlete was at the end of the run-up. For instance, a
point in the upper right part of the graph would
indicate a jump with a fast run-up but high COM at
the end of the run-up.
Let us consider what would happen if all the
athletes shown in Fig. 14.3 had similar dynamic
strength in the takeoff leg. In such a case, the
athletes in the upper left part of the graph would be
far from their limit for buckling, the athletes in the
lower right part of the graph would be closest to
buckling, and the athletes in the centre, lower left or
upper right parts of the graph would be somewhere
6.4
6.6
6.8
7.0
7.2
vH1 (m ·s–1)
7.4
7.6
7.8
8.0
in between with respect to buckling. Therefore, if all
the athletes shown in Fig. 14.3 had similar dynamic
strength, we would recommend the athletes in the
upper left part of the graph to learn how to run
faster and lower, and then experiment with jumps
using run-ups that are faster and/or lower than
their original ones. Athletes in the centre, lower left
and upper right parts of the graph would also be
advised to experiment with faster and lower runups, possibly emphasizing ‘faster’ for any jumpers
in the lower left part of the graph, and ‘lower’ for
jumpers in the upper right part of the graph. The
athletes in the lower right part of the graph would
be cautioned against the use of much faster and/or
lower run-ups than their present ones, because
these athletes would already be closer to buckling
than the others.
The procedure just described would make sense
if all the jumpers in Fig. 14.3 had similar dynamic
strength in the takeoff leg. However, this is unlikely.
Some high jumpers will be more powerful than others. Since stronger athletes can handle faster and
lower run-ups without buckling, it is possible that
an athlete in the upper left part of the graph might
be weak, and therefore close to buckling, while an
290
jumping and aerial movement
8.8
8.6
8.4
8.2
8.0
AVD
VH1 (m · s–1)
SOT
PAK
7.8
7.6
KOS SJO
AST
SOM
HEN BEY DRA
7.4
7.2
7.0
PAR
CON
FOR
STO
6.8
QUI
6.6
ZVA
6.4
6.2
ACU
6.0
5.8
3.2
3.4
3.6
3.8
4.0
4.2
vZTO (m·s–1)
4.4
athlete farther down and to the right in the graph
might be more powerful, and actually farther from
buckling. The optimum combination of run-up
speed and COM height will be different for different
high jumpers.
High jumpers with greater dynamic strength in
the takeoff leg will be able to handle faster and
lower run-ups without buckling during the takeoff
phase. However, it is not easy to measure the
‘dynamic strength’ of a high jumper’s takeoff leg.
The personal record of an athlete in a squat lift or in
a vertical jump-and-reach test are not good indicators. This is because these tests do not duplicate
closely enough the conditions of the high-jump
takeoff. Therefore, we used instead the vertical
velocity of the high jumper at the end of the takeoff
phase (vZTO—see below) as a rough indicator of the
dynamic strength of the takeoff leg. In other words,
we used the capability of a high jumper to generate lift in a high jump as a rough indicator of the
athlete’s dynamic strength or ‘takeoff power’.
To help us predict the optimum horizontal speed
at the end of the run-up, we made use of statistical
information accumulated through film analyses of
male and female high jumpers in the course of
Scientific Support Services work in the period
4.6
4.8
5.0
Fig. 14.4 Relationship between the
vertical velocity at the end of the
takeoff (vZTO) and the horizontal
velocity at the end of the run-up
(vH1).
1982–87 (Dapena et al. 1990). The athletes involved
in these studies were all elite high jumpers filmed at
the finals of national and international level competitions (USATF and NCAA Championships, US
Olympic Trials, World Indoor Championships).
Each small dot in Fig. 14.4 represents one jump
by one of the athletes in our statistical sample. The
other symbols show the athletes used here for illustration purposes. The horizontal axis of the graph
shows vertical velocity at takeoff (vZTO): The most
powerful high jumpers are those able to generate
most lift, and they are to the right in the graph; the
weaker jumpers are to the left. The vertical axis
shows the final speed of the run-up (vH1). The diagonal ‘regression’ line shows the trend of the statistical
data. The graph agrees with our expectations: The
more powerful jumpers, those able to generate more
lift (vZTO), can also handle faster run-ups (vH1) without buckling.
So, what is the optimum run-up speed for a given
high jumper? It seems safe to assume that highjumpers will rarely run so fast that the takeoff leg
will buckle. This is because it takes conscious effort
to use a fast run-up, and if the athlete feels that the
leg has buckled in one jump, an easier (slower) runup will be used in subsequent jumps. Since partial
the high jump
291
54
52
KOS
50
SOM
hTD (%)
ACU HEN
48
BEY
AST
PAR
SJO
FOR
DRA STO
QUI
ZVA
46
SOT
AVD
PAK
44
Fig. 14.5 Relationship between the
vertical velocity at the end of the
takeoff (vZTO) and the height of
the COM at the end of the run-up
(hTD, expressed as a percentage of
standing height).
CON
42
3.2
buckling will begin to occur at run-up speeds immediately faster than the optimum, few high jumpers
would be expected to regularly use run-ups that
are faster than their optimum. We should expect
a larger number of high jumpers to use run-up
speeds that are slower than their optimum. This is
because a fair number of high jumpers have not
learned to use a fast enough run-up. Therefore, the
diagonal regression line which marks the average
trend in the graph probably marks speeds that are
somewhat slower than the optimum. In summary,
although the precise value of the optimum run-up
speed is not known for any given value of vZTO , it is
probably faster than the value predicted by the
diagonal regression line; athletes near the regression line or below it were probably running too
slowly at the end of the run-up.
A similar rationale can be followed with the
graph of hTD vs. vZTO , shown in Fig. 14.5. Each small
dot in Fig. 14.5 represents one jump by one of the
athletes in our statistical sample. The horizontal axis
of the graph again shows vertical velocity at takeoff
(vZTO): the most powerful high jumpers are those
able to generate more lift, and they are to the right in
the graph; the weaker jumpers are to the left. The
vertical axis shows the height of the COM at the
3.4
3.6
3.8
4.0
4.2
vZTO (m ·s–1)
4.4
4.6
4.8
5.0
start of the takeoff phase (hTD). Although the data
are more ‘noisy’ than in the previous graph (there is
a wider ‘cloud’ around the regression line), the
graph in Fig. 14.5 also agrees with our general
expectations: The more powerful jumpers (larger
vZTO values) can be lower at the end of the run-up
(smaller hTD values) without buckling. In Fig. 14.5,
jumpers on the regression line or above it have
defective techniques, and the optimum will be somewhere below the regression line.
When Figs 14.4 and 14.5 are used as diagnostic
tools, it is necessary to take into consideration the
information from both graphs. For instance, if a
given athlete is near the regression lines in Figs 14.4
and 14.5, or below the regression line in Fig. 14.4 and
above the regression line in Fig. 14.5, we should presume that this athlete is not near the buckling point.
Therefore the athlete should be advised to increase
the run-up speed and/or to run with lower hips at
the end of the run-up. However, if an athlete is
slightly below the regression line in Fig. 14.4, but
markedly below it in Fig. 14.5, the situation is different. Since the COM was very low during the run-up,
maybe the athlete was close to the buckling point,
even though the run-up speed was not very fast. In
this case, it would not be appropriate to advise an
292
jumping and aerial movement
increase in run-up speed, even if the athlete was
running somewhat slower than we would expect.
Some caution is needed here. The use of a faster
and/or lower run-up will put a greater stress on
the takeoff leg, and thus may increase the risk of
injury if the leg is not strong enough. Therefore, it is
important to use caution in the adoption of a faster
and/or lower run-up. If the desired change is very
large, it would be advisable to make it gradually,
over a period of time. In all cases, it may be wise
to further strengthen the takeoff leg, so that it can
withstand the increased force of the impact produced when the takeoff leg is planted.
Vertical velocity of the COM at the start
of the takeoff phase
The vertical velocity at the end of the takeoff phase,
which is of crucial importance for the height of the
jump, is determined by the vertical velocity at the
start of the takeoff phase and by the change that
takes place in its value during the takeoff phase. In
normal high jumping, at the end of the run-up (i.e. at
the start of the takeoff phase) the athlete is moving
fast forwards, and also slightly downwards. In
other words, the vertical velocity at the start of the
takeoff phase (vZTD) usually has a small negative
value. It is evident that for a given change in vertical
velocity during the takeoff phase, the athlete with
the smallest amount of negative vertical velocity at
touchdown will jump the highest. The values of
vZTD are shown in Table 14.3. The jumpers with the
best techniques in this respect are those with the
least negative vZTD values.
In each step of the run-up the COM normally
moves up slightly as the athlete takes off from the
ground, reaches a maximum height, and then drops
down again before the athlete plants the next foot on
the ground. In the last step of the run-up, if the takeoff foot is planted on the ground early, the takeoff
phase will start before the COM acquires too much
downward vertical velocity. To achieve this, the
athlete has to try to make the last two foot contacts
with the ground very quickly one after the other. In
other words, the tempo of the last two foot supports
should be very fast.
If the length of the last step is very long, it could
contribute to a late planting of the takeoff foot, and
therefore to a large negative value for vZTD. Table
14.2 shows the length of the last step of the run-up
(SL1). This length is expressed in metres, but to
facilitate comparisons among athletes it is also
expressed as a percentage of the standing height of
the athlete.
Another factor that influences the vertical velocity at the start of the takeoff phase is the way in
which the COM is lowered in the final part of the
run-up. High-jumpers can be classified into three
groups, depending on the way in which they lower
the COM. Many athletes lower their COM early
(two or three steps before the takeoff), and then
move more or less flat in the last step. These athletes
typically have a moderate amount of downward
vertical velocity at the instant that the takeoff phase
starts. The second group of athletes keep their hips
high until almost the very end of the run-up, and
then they lower the COM in the last step. These athletes have a large negative vertical velocity at the
start of the takeoff phase, regardless of how early
they plant the takeoff foot on the ground. A third
group of athletes lower the COM in the same way as
the first group, but then raise it again quite a bit as
the non-takeoff leg pushes off into the last step.
These athletes typically have a very small amount of
downward vertical velocity at the start of the takeoff
phase, which is good, but they also waste part of
their previous lowering of the COM.
The first and the third techniques have both
advantages and disadvantages, but the second technique seems to be less sound than the other two,
because of the large downward vertical velocity that
it produces at the instant of the start of the takeoff
phase.
Orientation of the takeoff foot and
potential for ankle and foot injuries
At the end of the run-up, the high jumper’s COM is
moving at an angle p1 with respect to the bar (see
‘Approach angles’ above). During the takeoff phase,
the athlete pushes on the ground vertically downwards, and also horizontally. The horizontal force
that the foot makes on the ground during the takeoff
phase points forwards, almost in line with the final
the high jump
293
Landing pit
Bar
Final direction
of the run-up
Horizontal force made
on the ground
e3
Longitudinal axis
of the foot
p1
e2
e1
Fig. 14.6 Angles of foot, of run-up
direction, and of horizontal force
(see text).
direction of the run-up, but usually it is also deviated slightly towards the landing pit (see Fig. 14.6).
Most high jumpers plant the takeoff foot on the
ground with its longitudinal axis pointing in a direction that generally is not aligned with the final direction of the run-up nor with the horizontal force that
the athlete is about to make on the ground: It is more
parallel to the bar than either one of them. Since the
horizontal reaction force that the foot receives from
the ground is not aligned with the longitudinal axis
of the foot, the force tends to make the foot roll
inwards. (See the sequence in Fig. 14.7, obtained
from a high-speed videotape taken during the 1988
International Golden High Jump Gala competition
in Genk, Belgium—courtesy of B. Van Gheluwe.)
In anatomical terminology, this rotation is called
‘pronation of the ankle joint’. It stretches the medial
side of the joint, and produces compression in the
lateral side of the joint. If the pronation is very
severe, it can lead to injury of the ankle. It also
means that the foot becomes supported less by
its outside edge, and more by the longitudinal
Horizontal reaction force
received by the foot
e3
(forward–backward) arch on the medial side of the
foot. According to Krahl and Knebel (1979), this can
lead to injury of the foot itself.
Pronation of the ankle joint occurs in the takeoffs
of many high jumpers. However, it is difficult to see
without a very magnified image of the foot. Because
of this, pronation of the ankle joint generally is not
visible in our standard films or videotapes of highjumping competitions (and therefore it does not
show in our computer graphics sequences either).
This does not mean that there is no ankle pronation;
we just cannot see it.
In an effort to diagnose the risk of ankle and foot
injury for each high jumper, we measure angles e1
(the angle between the longitudinal axis of the foot
and the bar), e2 (between the longitudinal axis of the
foot and the final direction of the run-up) and e3
(between the longitudinal axis of the foot and the
horizontal force) in each jump (see Fig. 14.6). The
values of these angles are reported in Table 14.2. For
diagnosing the risk of injury, e3 is the most important angle. Although the safety limit is not known
294
jumping and aerial movement
with certainty at this time, anecdotal evidence suggests that e3 values smaller than 20° are reasonably
safe, values between 20 and 25° are somewhat risky,
and values larger than 25° are dangerous.
Trunk lean
Fig. 14.7 Ankle pronation during the takeoff phase.
(Videotape courtesy of B. Van Gheluwe.)
Figure 14.8 shows BFTD, BFTO, LRTD and LRTO,
the backward/forward and left/right angles of lean
of the trunk at the start and the end of the takeoff
phase, respectively. The values of these angles are
given in Table 14.4. The trunk normally has a backward lean at the start of the takeoff phase (BFTD).
Then it rotates forwards, and by the end of the takeoff it is close to vertical, and sometimes past the vertical (BFTO). Due to the curved run-up, the trunk
normally has also a lateral lean towards the centre of
the curve at the start of the takeoff phase (LRTD).
During the takeoff phase, the trunk rotates towards
the right (towards the left in athletes who take off
from the right foot), and by the end of the takeoff it is
usually somewhat beyond the vertical (LRTO)—
up to 10° beyond the vertical (LRTO = 100°) may
be considered normal. Table 14.4 also shows the
values of ∆BF and ∆LR. These are the changes
that occur during the takeoff phase in the backward/forward and left/right angles of tilt of the
trunk, respectively.
Statistical information (Dapena, unpublished
observations) shows a relationship of the trunk lean
angles with the vertical velocity of the athlete at the
end of the takeoff phase, and consequently with the
peak height of the COM. If two athletes have similar
run-up speed, height of the COM at the end of the
run-up and arm actions during the takeoff phase
(see below), the athlete with smaller BFTD, ∆BF,
LRTD and ∆LR values generally obtains a larger
vertical velocity by the end of the takeoff phase. This
means that athletes with greater backward lean at
the start of the takeoff phase and greater lateral lean
towards the centre of the curve at the start of the
takeoff phase tend to jump higher. Also, for a given
amount of backward lean at the start of the takeoff
phase, the athletes who experience smaller changes
in this angle during the takeoff phase generally
jump higher, and for a given amount of lateral lean
at the start of the takeoff phase, the athletes who
the high jump
295
Side view
BFTO
BFTD
Back view
LRTO
LRTD
Fig. 14.8 Backward/forward (BF)
and left/right (LR) tilt angles of the
trunk at the start (TD) and at the end
(TO) of the takeoff phase.
experience smaller changes in this angle during the
takeoff phase also tend to jump higher.
However, before jumping to conclusions and
deciding that all high jumpers should lean backwards and laterally as much as possible at the start
of the takeoff phase, and then change those angles of
lean as little as possible during the takeoff phase
itself, it is necessary to take two points into consideration. Firstly, small values of BFTD, ∆BF, LRTD
and ∆LR are not only statistically associated with
larger vertical velocities at the end of the takeoff
phase (which is good), but also with less angular
momentum (see below), and therefore with a less
effective rotation during the bar clearance.
Also, we cannot be completely certain that small
values of BFTD, ∆BF, LRTD and ∆LR produce a takeoff that generates a larger amount of vertical velocity and therefore a higher peak height for the COM
We do not understand well the cause– effect mechanisms behind the statistical relationships, and it is
possible to offer alternative explanations, such as
the following. Weaker athletes are not able to generate much lift, mainly because they are weak.
Therefore, they are not able to jump very high. This
296
jumping and aerial movement
Table 14.4 Angles of tilt of the trunk [backward/forward at the start of the takeoff phase (BFTD) and at the end of the
takeoff phase (BFTO) and the change in this angle during the takeoff phase (∆BF); left/right at the start of the takeoff
phase (LRTD) and at the end of the takeoff phase (LRTO), and the change in this angle during the takeoff phase (∆LR)],
activeness of the arm nearest to the bar (AAN) and of the arm farthest from the bar (AAF), summed activeness of the two
arms (AAT), activeness of the lead leg (LLA), and summed activeness of the three free limbs (FLA).
Athlete
BFTD BFTO ∆BF
(°)
(°)
(°)
LRTD LRTO ∆LR AAN
AAF
AAT
LLA
FLA
(°)
(°)
(°)
(mm · m−1) (mm · m−1) (mm · m−1) (mm · m−1) (mm · m−1)
Men
Avdeyenko
Conway
Forsyth
Paklin
Partyka
Sjöberg
Sotomayor
Stones
Zvara
71
76
71
77
75
74
71
74
68
92
83
86
81
89
88
77
90
83
21
7
15
5
14
15
5
16
15
76
79
76
77
76
75
79
73
77
104
95
104
99
92
98
101
91
95
28
16
28
22
16
23
22
19
18
4.3
6.7
10.0
5.3
3.3
6.7
5.9
3.4
9.0
10.5
12.2
10.7
8.9
7.1
10.0
10.8
8.3
13.3
14.8
18.9
20.8
14.2
10.4
16.7
16.7
11.7
22.3
24.0
21.2
24.9
14.1
15.4
18.7
24.5
18.3
41.7
38.7
40.2
45.6
28.2
25.8
35.4
41.2
30.0
64.0
Women
Acuff
Astafei
Beyer-Helm
Dragieva
Henkel
Kostadinova
Quintero
Sommer
73
77
79
76
82
73
73
80
87
82
94
82
90
84
91
90
14
5
15
6
8
12
18
10
78
84
74
80
75
77
79
81
92
102
96
92
97
93
104
99
14
18
23
12
22
17
26
18
0.5
3.6
2.3
1.3
5.9
−0.4
4.4
2.2
7.1
6.6
7.0
7.3
8.3
6.2
10.0
4.9
7.5
10.2
9.3
8.5
14.2
5.8
14.4
7.1
19.1
13.5
15.6
21.8
19.3
21.0
18.2
17.8
26.6
23.7
24.9
30.4
33.4
26.8
32.7
24.9
Note: Some of the values in this table may not fit perfectly with each other, because of rounding off.
makes them reach the peak of the jump relatively
soon after takeoff. Consequently, they will want to
rotate faster in the air to reach a normal horizontal
layout position at the peak of the jump. For this,
they will generate more angular momentum during
the takeoff, which in turn will require larger values
of BFTD, ∆BF, LRTD and ∆LR. We cannot be sure
which interpretation is the correct one: does the
trunk tilt affect the height of the jump, or does the
weakness of the athlete affect the height of the jump
and (indirectly) the trunk tilt? Or are both explanations partly correct? At this point, we do not know
for sure.
Arm and lead leg actions
The actions of the arms and of the lead leg during
the takeoff phase are important for the outcome
of the jump. As these free limbs are accelerated
upwards during the takeoff phase, they exert by
reaction a compressive force downwards on the
trunk. This helps the takeoff leg to exert a larger
force on the ground. The increased downward
vertical force exerted on the ground evokes by
reaction an increased upward vertical force exerted
by the ground on the athlete. This produces a
larger vertical velocity of the COM of the athlete by
the end of the takeoff phase, and consequently a
higher jump.
There is no perfect way to measure how active the
arms and the lead leg are during the takeoff phase of
a high jump. Currently, we express arm activeness
as the vertical range of motion of the COM of each
arm during the takeoff phase (relative to the upper
end of the trunk), multiplied by the fraction of the
whole body mass that corresponds to the arm, and
the high jump
divided by the standing height of the subject. The
activeness of the lead leg is similarly measured as
the vertical range of motion of the COM of the lead
leg during the takeoff phase (relative to the lower
end of the trunk), multiplied by the fraction of the
whole body mass that corresponds to the lead leg,
and divided by the standing height of the subject. In
effect, this means that the activeness of each free
limb is expressed as the number of millimetres contributed by the limb motion to the lifting of the COM
of the whole body during the takeoff phase, per
metre of standing height. Defined in this way, the
activeness of each free limb takes into account the
limb’s mass, its average vertical velocity during
the takeoff phase, and the duration of this vertical
motion. It allows the comparison of one jumper
with another, and also direct comparison of the lead
leg action with the arm actions.
Table 14.4 shows the activeness of the arm nearest
to the bar (AAN) and of the arm farthest from the
bar (AAF), the summed activeness of the two arms
14
ZVA
25
12
CON
FOR
AVD
QUI
SJO
PAK
8
KOS
20
STO
HEN
DRA
ACU
BEY
PAR
AST
15
6
–1
)
AAF (mm· m–1)
10
SOT
AT
10
A
4
(m
m
·m
SOM
2
5
0
2
4
6
8
AAN (mm·m–1)
10
12
Fig. 14.9 Activeness of the arm nearest to the bar (AAN),
of the arm farthest from the bar (AAF), and combined
activeness of both arms (AAT).
297
(AAT), the activeness of the lead leg (LLA) and the
combined activeness of all three free limbs (FLA).
Larger values indicate greater activeness of the
limbs during the takeoff.
Figure 14.9 shows a plot of AAF vs. AAN for the
sample jumps. The ideal is to be as far to the right
and as high up as possible on the graph, as this gives
the largest values for the total arm action, AAT, also
shown in the graph.
For a good arm action, both arms should swing
strongly forwards and upwards during the takeoff
phase. They should not be too flexed at the elbow
during the swing—a good elbow angle seems to
be somewhere between full extension and 90° of
flexion.
The diagonal line going from lower left to upper
right in Fig. 14.9 indicates the points for which
both arms would have equal activeness. The positions of the points above the diagonal line reflect
a well-established fact: high jumpers are generally
more active with the arm that is farthest from the
bar.
Some high jumpers (including many women) fail
to prepare their arms correctly in the last steps of the
run-up, and at the beginning of the takeoff phase the
arm nearest to the bar is ahead of the body instead
of behind it. From this position the arm is not able
to swing strongly forwards and upwards during
the takeoff, and these jumpers usually end up with
small (or even negative) AAN values. These athletes
should learn to bring both arms back in the final one
or two steps of the run-up, so that both arms can
later swing hard forwards and up during the takeoff
phase. Learning this kind of arm action will take
some time and effort, but it should produce a higher
jump. If an athlete is unable to prepare the arms for a
double-arm action, the forward arm should be in a
low position at the start of the takeoff phase. That
way, it can be thrown upwards during the takeoff,
although usually not quite as hard as with a doublearm action.
Figure 14.10 shows a plot of LLA vs. AAT for the
trials in the sample. The ideal is to be as far to the
right and as high up as possible on the graph, as this
gives the largest values for the total free limb action,
FLA, also shown in the graph.
298
jumping and aerial movement
45
ZVA
60
40
35
AVD
ACU
HEN
50
DRA
KOS
BEY
15
STO
PAR
AST
CON
QUI SJO
m –1
) 4
0
SOM
PAK
10
5
FLA
20
30
10
m·
20
FOR
SOT
25
(m
LLA (mm ·m–1)
30
0
5
10
15
AAT (mm·m–1)
Takeoff time
The duration of the takeoff phase (TTO) is shown in
Table 14.5. (Due to the slow camera speeds used, the
value of TTO can easily be in error by 0.01 s, and
sometimes by as much as 0.02 s.) This ‘takeoff time’
is influenced by a series of factors. Some of them are
beneficial for the jump; others are detrimental. Short
takeoff times go together with a strong action of the
takeoff leg (good), but also with weak arm actions
and with a high COM position at the start of the
takeoff phase (bad). In summary, takeoff times are
informative, but the length of the takeoff time by
itself does not necessarily indicate good or bad
technique.
Change in horizontal velocity during
the takeoff phase
It was explained before that the athlete should have
a large horizontal velocity at the instant immediately before the takeoff foot is planted on the ground
to start the takeoff phase, and that therefore no hori-
20
25
Fig. 14.10 Combined activeness of
both arms (AAT), activeness of the
lead leg (LLA), and total activeness of
the free limbs (FLA).
zontal velocity should be lost before that instant.
However, the horizontal velocity should be reduced
considerably during the takeoff phase itself. The
losses of horizontal velocity that all high jumpers
experience during the takeoff phase (see ∆vH in
Table 14.3) are due to the fact that the jumper pushes
forwards on the ground during the takeoff phase,
and therefore receives a backward reaction force
from the ground. These losses of horizontal velocity
during the takeoff phase are an intrinsic part of the
takeoff process, and they are associated with the
generation of vertical velocity. If an athlete does not
lose much horizontal velocity during the takeoff
phase, this may be a sign that the athlete is not making good use of the horizontal velocity obtained
during the run-up. We could say that the athlete
should produce a lot of horizontal velocity during
the run-up so that it can then be lost during the
takeoff phase while the athlete obtains vertical
velocity. If not enough horizontal velocity is produced during the run-up, or not enough is lost
during the takeoff, the run-up is not being used
appropriately to help the athlete to jump higher.
the high jump
299
Table 14.5 Takeoff time (TTO), height of the bar (hBAR), maximum height of the centre of mass (COM) (hPK), clearance
height in the plane of the standards (hCLS), absolute clearance height (hCLA), effectiveness of the bar clearance in the plane
of the standards (∆hCLS), and absolute effectiveness of the bar clearance (∆hCLA); twisting angular momentum (HT),
forward somersaulting angular momentum (HF), lateral somersaulting angular momentum (HL) and total somersaulting
angular momentum (HS) during the airborne phase.
Athlete
TTO
(s)
hBAR
(m)
hPK
(m)
hCLS
(m)
hCLA
(m)
∆hCLS
(m)
∆hCLA
(m)
HT
(*)
HF
(*)
HL
(*)
HS
(*)
Men
Avdeyenko
Conway
Forsyth
Paklin
Partyka
Sjöberg
Sotomayor
Stones
Zvara
0.21
0.18
0.17
0.20
0.15
0.16
0.17
0.17
0.23
2.38
2.34
2.34
2.38
2.34
2.34
2.34
2.34
2.34
2.46
2.41
2.44
2.41
2.39
2.33
2.44
2.36
2.46
2.41
2.33
2.35
2.40
2.36
2.35
2.36
2.29
2.36
2.42
2.35
2.39
2.41
2.36
2.35
2.39
2.29
2.36
−0.05
−0.08
−0.09
−0.01
−0.03
0.02
−0.08
−0.07
−0.10
−0.04
−0.06
−0.05
0.00
−0.03
0.02
−0.05
−0.07
−0.10
40
45
45
45
40
40
60
35
75
75
40
60
75
80
70
5
60
50
80
85
80
80
90
85
100
85
80
110
90
100
110
120
110
100
105
95
Women
Acuff
Astafei
Beyer-Helm
Dragieva
Henkel
Kostadinova
Quintero
Sommer
0.18
0.15
0.16
0.15
0.14
0.14
0.17
0.14
1.96
2.00
1.97
2.00
2.02
2.05
1.97
1.96
2.07
2.09
2.06
2.06
2.06
2.09
2.04
1.99
1.97
2.00
2.00
2.00
2.05
2.09
1.97
1.94
1.97
2.01
2.03
2.00
2.05
2.09
1.97
1.95
−0.10
−0.09
−0.06
−0.06
−0.01
0.00
−0.07
−0.05
−0.10
−0.08
−0.03
−0.06
−0.01
0.00
−0.07
−0.04
30
50
45
40
45
60
40
45
95
35
80
95
80
90
55
105
80
90
85
70
85
100
90
85
125
100
115
115
120
135
105
130
Note: Some of the values in this table may not fit perfectly with each other, because of rounding off.
* Angular momentum units: s−1 × 10 −3.
Height and vertical velocity of the COM
at the end of the takeoff phase
The peak height that the COM will reach over the
bar is completely determined by the end of the
takeoff phase. It is determined by the height and
the vertical velocity of the COM at the end of the
takeoff phase.
At the instant that the takeoff foot loses contact
with the ground, the COM of a high jumper is usually at a height somewhere between 68% and 73% of
the standing height of the athlete. This means that
tall high jumpers have a built-in advantage: their
centres of gravity will generally be higher at the
instant that they leave the ground.
The vertical velocity of the COM at the end of the
takeoff phase (vZTO, shown in Table 14.3) determines
how much higher the COM will travel beyond the
takeoff height after the athlete leaves the ground.
Height of the bar, peak height of
the COM, and clearance height
The height of the bar (hBAR) and the maximum
height reached by the COM (hPK) are shown in Table
14.5. All of the jumps shown here were successful
clearances.
The true value of a high jump generally is not
known: If the bar is knocked down, the jump is
ruled a foul and the athlete gets zero credit, even
though a hypothetical bar set at a lower height
would have been cleared successfully; if the bar
stays up, the athlete is credited with the height at
which the bar was set, ignoring whether the jumper
300
jumping and aerial movement
Fig. 14.11 Three images of a bar clearance.
Fig. 14.12 All the images of a bar clearance available from
film analysis.
had room to spare over it or whether the jumper
depressed the bar during the clearance.
Using computer modelling and graphics, it is possible to estimate the approximate maximum height
that an athlete would have been able to clear cleanly
without touching the bar in a given jump (‘clearance
height’), regardless of whether the actual jump was
officially a valid clearance or a foul. Figure 14.11
shows three images of a high jumper’s clearance of a
bar set at 2.25 m. Figure 14.12 shows all the images
obtained through film analysis of the bar clearance.
In Fig. 14.13 the drawing has been saturated with
intermediate positions of the high jumper, calculated through a process called curvilinear interpolation. The scale in the ‘saturation drawing’ shows
that in this jump the athlete would have been able to
clear a bar set in the plane of the standards at a
height of 2.34 m (hCLS) without touching it. A closer
examination of Fig. 14.13 also shows that the maximum height of the ‘hollow’ area below the body
was not perfectly centred over the bar: If this athlete
had taken off closer to the plane of the standards,
he would have been able to clear a bar set at an
absolute maximum height of 2.35 m (hCLA) without
touching it.
Due to errors in the measurements taken from the
films or videotapes, in the thicknesses of the various
body segments of the computer graphics model and
in the degree of curvature of the trunk in the drawings, the value of the clearance height in the plane of
the standards (hCLS) and the value of the absolute
clearance height (hCLA) obtained using this method
are not perfectly accurate. A test showed that the
true value of hCLS will be over- or underestimated on
average by between 0.02 m and 0.03 m. Therefore,
the calculated clearance height values should be
considered only rough estimates. Another point to
consider is that high jumpers can generally depress
the fibreglass bar by about 0.02 m (and sometimes
by as much as 0.04 or even 0.06 m) without knocking it down.
Table 14.5 shows the maximum height that the
athlete would have been able to clear without touching the bar in the plane of the standards (hCLS)
the high jump
301
3.00 m
2.00 m
1.00 m
Fig. 14.13 Graph of a bar clearance
produced through saturation with
interpolated images.
and the absolute maximum height that the athlete
would have been able to clear without touching the
bar (hCLA).
The differences between the clearance heights
and the peak height of the COM indicate the effectiveness of the bar clearance in the plane of the
standards (∆hCLS = hCLS – hPK) and the absolute
effectiveness of the bar clearance (∆hCLA = hCLA –
hPK). Table 14.5 shows their values in the sample trials. Larger negative numbers indicate less effective
bar clearances.
The main reasons for an ineffective bar clearance are: taking off too close or too far from the
bar, insufficient amount of somersaulting angular
momentum, insufficient twist rotation, poor arching, and bad timing of the arching/un-arching
process. These aspects of high jumping technique
will be discussed next.
Takeoff distance
The distance between the toe of the takeoff foot and
the plane of the bar and the standards is called the
‘takeoff distance’ (TOD in Fig. 14.2). The value of
this distance is shown in Table 14.2, and it is important because it determines the position of the peak of
the jump relative to the bar: If an athlete takes off too
far from the bar, the COM will reach its maximum
height before crossing the plane of the standards,
and the jumper will probably fall on the bar; if the
athlete takes off too close to the bar, there will be
a large risk of hitting the bar while the COM is on
302
jumping and aerial movement
the way up, before reaching its maximum height.
Different athletes usually need different takeoff distances. The optimum value for the takeoff distance
of each athlete is the one that will make the COM
of the jumper reach its maximum height more or
less directly over the bar, and it will depend primarily on the final direction of the run-up and on the
amount of residual horizontal velocity that the
athlete has left after the completion of the takeoff
phase.
In general, athletes who travel more perpendicular to the bar in the final steps of the run-up (indicated by large p2 and p1 angles in Table 14.2) will
also travel more perpendicular to the bar after the
completion of the takeoff phase (indicated by large
p0 angles in Table 14.2), and they will need to take
off farther from the bar. In general, athletes who run
faster in the final steps of the run-up (indicated
by large values of vH2 and vH1 in Table 14.3) will
also have more horizontal velocity left after takeoff
(indicated by large values of vHTO in Table 14.3);
thus, they will travel through larger horizontal distances after the completion of the takeoff than
slower jumpers, and they will also need to take off
farther from the bar in order for the COM to reach its
maximum height more or less directly over the bar.
High jumpers need to be able to judge after a miss
whether the takeoff point might have been too close
or too far from the bar. This can be done by paying
attention to the time when the bar was hit. If the bar
was hit a long time after the takeoff, this probably
means that the bar was hit as the athlete was coming
down from the peak of the jump, implying that the
athlete took off too far from the bar, and in that case
the athlete should move the starting point of the
run-up slightly closer to the bar; if the bar was hit
very soon after takeoff, this probably means that the
bar was hit while the athlete was still on the way up
towards the peak of the jump, implying that the
takeoff point was too close to the bar, and in that
case the athlete should move the starting point of
the run-up slightly farther from the bar.
Angular momentum
Angular momentum (or ‘rotary momentum’) is a
mechanical factor that makes the athlete rotate.
High jumpers need the right amount of angular
momentum to make in the air the rotations necessary for a proper bar clearance. The athlete obtains
the angular momentum during the takeoff phase,
through the forces that the takeoff foot makes on the
ground; the angular momentum cannot be changed
after the athlete leaves the ground.
The bar clearance technique of a Fosbury-flop can
be described roughly as a twisting somersault. To a
great extent, the twist rotation (which makes the
athlete turn his or her back to the bar during the
ascending part of the flight path) is generated by
swinging the lead leg up and somewhat away from
the bar during the takeoff, and also by actively turning the shoulders and arms during the takeoff in the
desired direction of the twist. These actions create
angular momentum about a vertical axis. This is
called the twisting angular momentum, HT. The HT
values of the analysed athletes are shown in Table
14.5. (To facilitate comparisons among athletes, the
angular momentum values have been normalized
for the mass and standing height of each athlete.)
Most high jumpers have no difficulty obtaining an
appropriate amount of HT. (However, we will see
later that the actions that the athlete makes in the air,
as well as other factors, can also significantly affect
whether the high jumper will be perfectly face-up at
the peak of the jump, or tilted to one side with one
hip lower than the other.)
The somersault rotation, which will make the
shoulders go down while the knees go up, results
from two components: a forward somersaulting
component and a lateral somersaulting component.
Forward somersaulting angular momentum (H F)
During the takeoff phase, the athlete produces
angular momentum about a horizontal axis perpendicular to the final direction of the run-up (see
Fig. 14.14a and the sequence at the top of Fig. 14.15).
This forward rotation is similar to the one produced when a person hops off from a moving bus
facing the direction of motion of the bus: After the
feet hit the ground, the tendency is to rotate forward
and fall flat on one’s face. It can be described as
angular momentum produced by the checking of a
linear motion.
the high jump
Side view
303
Back view
HL
HF
(a)
(b)
Overhead view
Final run-up
direction
Lateral
HL somersaulting
rotation
Fig. 14.14 (a) Forward somersaulting
angular momentum; (b) lateral
somersaulting angular momentum;
(c) resultant somersaulting angular
momentum.
Resultant
HS somersaulting
rotation
(c)
The tilt angles of the trunk at the start and at the
end of the takeoff phase (see ‘Trunk lean’ above)
are statistically related to the angular momentum
obtained by the athlete ( J. Dapena, unpublished
observations). Large changes of the trunk tilt from
a backward position towards vertical during the
takeoff phase are associated with a larger amount
of forward somersaulting angular momentum. This
makes sense, because athletes with a large amount
of forward somersaulting angular momentum at the
end of the takeoff phase should also be expected to
have a large amount of it already during the takeoff
phase, and this should contribute to a larger forward rotation of the body in general and of the
trunk during the takeoff phase.
Forward
HF somersaulting
rotation
Statistics show that jumpers with a very large backward lean at the start of the takeoff phase (small
BFTD angles) do not get quite as much forward
somersaulting angular momentum as other jumpers.
The reasons for this are not completely clear.
The forward somersaulting angular momentum
can also be affected by the actions of the arms and
lead leg. Wide swings of the arms and of the lead leg
during the takeoff can help the athlete to jump
higher (see ‘Arm and lead leg actions’ above).
However, in a view from the side (top sequence in
Fig. 14.16) they also imply backward (clockwise)
rotations of these limbs, which can reduce the total
forward somersaulting angular momentum of the
body.
304
jumping and aerial movement
Side view
Back view
10.22
10.20
10.18
10.16
10.14
10.12
10.10
10.08
10.06
10.04
10.02
10.00
Fig. 14.15 Side and back views of the takeoff of a standard jump. To facilitate the comparison of one jump with another,
the value t = 10.00 s is arbitrarily assigned in all jumps to the instant at which the takeoff foot first makes contact with the
ground to start the takeoff phase.
Side view
Back view
10.22
10.20
10.18
10.16
10.14
10.12
10.10
10.08
10.06
10.04
10.02
10.00
Fig. 14.16 Side and back views of the takeoff of a jump with direct forward arm swing.
To lessen this problem, some high jumpers turn
their back partly towards the bar in the last step of
the run-up, and then swing the arms diagonally forwards and away from the bar during the takeoff
phase (see Fig. 14.17). Since this diagonal arm swing
is not a perfect backward rotation, it interferes less
with the generation of forward somersaulting angular momentum.
the high jump
305
Side view
Back view
10.22
10.20
10.18
10.16
10.14
10.12
10.10
10.08
10.06
10.04
10.02
10.00
Fig. 14.17 Side and back views of the takeoff of a jump with diagonal arm swing.
Lateral somersaulting angular momentum (HL)
During the takeoff phase, angular momentum is also
produced about a horizontal axis in line with the final
direction of the run-up (see Fig. 14.14b and the bottom
sequence in Fig. 14.15). In a rear view of an athlete
who takes off from the left leg, this angular momentum component appears as a clockwise rotation.
If the jumper made use of a straight run-up, in a
rear view the athlete would be upright at touchdown, and leaning towards the bar at the end of the
takeoff. Since a leaning position would result in a
lower height of the COM at the end of the takeoff
phase, the production of angular momentum would
thus cause a reduction in the vertical range of
motion of the COM during the takeoff phase.
However, if the athlete uses a curved run-up, the
initial lean of the athlete to the left at the end of the
approach run may allow the athlete to be upright at
the end of the takeoff phase (see Fig. 14.14b and the
bottom sequence in Fig. 14.15). The final upright
position contributes to a higher COM position at the
end of the takeoff phase. Also, the initial lateral tilt
contributes to a lower COM position at the start of
the takeoff phase. Therefore the curved run-up,
together with the generation of lateral somersaulting angular momentum, contributes to increase the
vertical range of motion of the COM during the
takeoff phase, and thus permits greater lift than if a
straight run-up were used. (However, some caution
is necessary here, since statistical information suggests that jumpers with an excessive lean towards
the centre of the curve at the start of the takeoff
phase tend to generate a smaller amount of lateral
somersaulting angular momentum than jumpers
with a more moderate lean. The reasons for this are
not clear.)
There is some statistical association between large
changes in the left/right tilt angle of the trunk during the takeoff phase and large amounts of lateral
somersaulting angular momentum at the end of
the takeoff phase ( J. Dapena, unpublished observations). This makes sense, because athletes with
a large amount of lateral somersaulting angular
momentum at the end of the takeoff phase should
also be expected to have a large amount of it already
during the takeoff phase, which should contribute
to a larger rotation of the trunk during the takeoff
phase from its initial lateral tilted position toward
the vertical.
306
jumping and aerial movement
140
120
100
SOT
ZVA
CON
KOS
STO PAK HEN
BEY
SJO
SOM
FOR
AVD
ACU
HL
80
PAR
QUI
AST
DRA
60
140
40
120
100
80
HS
20
0
20
40
60
80
100
HF
The reader should be reminded at this point that
although large changes in tilt during the takeoff
phase and, to a certain extent, small backward and
lateral leans of the trunk at the start of the takeoff
phase (i.e. large BFTD and LRTD values) are associated with increased angular momentum, they are
also statistically associated with reduced vertical
velocity at the end of the takeoff phase, and therefore with a reduced maximum height of the COM at
the peak of the jump. This supports the intuitive
feeling of high jumpers that it is necessary to seek a
compromise between the generation of lift and the
generation of rotation.
The bottom sequence in Fig. 14.17 shows that in
an athlete who takes off from the left leg a diagonal
arm swing is associated with a clockwise motion of
the arms in a view from the back, and therefore it
contributes to the generation of lateral somersaulting angular momentum.
High jumpers usually have more lateral than forward somersaulting angular momentum. The sum
of these two angular momentum components adds
120
140
Fig. 14.18 Forward (HF), lateral (HL)
and total (HS) somersaulting angular
momentum.
up to the required total (or ‘resultant’) somersaulting angular momentum, HS (Fig. 14.14c).
The forward (HF), lateral (HL) and total (HS)
somersaulting angular momentum values of the
analysed athletes are shown in Table 14.5, and in
graphical form in Fig. 14.18. In general, athletes with
more angular momentum tend to rotate faster.
Female high jumpers tend to acquire more angular momentum than male high jumpers. This is
because the women do not jump quite as high, and
therefore they need to rotate faster to compensate
for the smaller amount of time available between
the takeoff and the peak of the jump.
Adjustments in the air
After the takeoff is completed, the path of the COM
is totally determined, and there is nothing that the
athlete can do to change it. However, this does not
mean that the paths of all parts of the body are determined. What cannot be changed is the path of the
point that represents the average position of all the
the high jump
307
(a)
(b)
(c)
10.94
10.82
10.70
10.58
10.46
10.34
10.22
Fig. 14.19 Bar clearance sequences of three jumps (see text).
body parts (the COM), but it is possible to move one
part of the body in one direction if other parts are
moved in the opposite direction. Using this principle, after the shoulders pass over the bar the
high jumper can raise the hips by lowering the
head and the legs. For a given position of the COM,
the farther the head and the legs are lowered, the
higher the hips will be lifted. This is the reason for
the arched position on top of the bar.
To a great extent, the rotation of the high jumper
in the air is also determined once the takeoff phase is
completed, because the angular momentum cannot
be changed during the airborne phase. However,
some alterations of the rotation are still possible. By
slowing down the rotations of some parts of the
body, other parts of the body will speed up as a
compensation, and vice versa. For instance, the athlete shown in Fig. 14.19a slowed down (and even
reversed) the counterclockwise rotation of the take-
off leg shortly after the ta